Although the majority of Lost has been well received, several different elements have received much criticism.
When Ana Lucia Cortez became a main character in Season 2, producers found many fans disliked the character. Her "tough girl" attitude turned many people off, along with her accidental killing of Shannon.  The producers claimed that her character would "arc", which she did right before she was killed off in "Two for the Road". Long before the episode even aired, though, an insider claimed that the producers were fed up with Rodriguez's behavior, both on and off set and that she would be killed off, like Maggie Grace, who was also rumored to be difficult to work with.   Lost producers denied rumors that she was killed off because of Ana Lucia's unpopularity or that Michelle Rodriguez was frustrating to work with. The main rumor seemed to be that Ana Lucia (as well as Libby) were killed off because the actors who played them, Rodriguez and Cynthia Watros, were arrested for drunk driving in December 2005.   Rodriguez pleaded not guilty, and was sentenced to five days in jail.  Michelle only served sixty-five hours of her jail sentence, before being let out due to jail over-crowding. Producers denied that Ana Lucia would be killed off because Rodriguez had a DUI and jail time even before she was killed off; they claim that Ana's death was planned when Rodriguez was cast, because Rodriguez had a "nomadic spirit" and didn't want to be on the show for more than a year. 
Michael's frequent screaming and obsession for his son was noteworthy and frequent enough for it to grate on the audience.
Many fans have voiced their annoyance of the lack of information provided for the character, especially with the wasted opportunity when Cynthia Watros appeared as a Special Guest Star in "Meet Kevin Johnson".
Other In-Show Criticisms
"I just wonder, going forward, if the flashbacks will begin to seem like crutches, somewhat repetitive fare that occupies much of the hour while the Island stories go forward verrrry slowly."-Maureen Ryan, critic 
After the first season, many viewers of the show began to grow tired of the flashbacks. They were perceived by some to be repetitive and recycling information we were already aware of; flashbacks have gotten less important than they were in the first season, taking away from the on-island storylines. The producers have found new ways to make flashbacks interesting, such as flashbacks of on-island incidents, both before and during the main protagonists time on the island and, from the end of season 3 onwards, flash forwards.
"There’s been a pervading sense that the creators really don’t know what the hell is going on, and that they’re just as surprised to find out what’s happening as the audience is."-Steven Simunic, critic 
Many complain that Lost is moving too slowly and there is a lack of answers in the show. This has turned many people off and even Lost fans over time.  Typically, Season Two of Lost has been under fire the most for having little or no action in most episodes.   The season three premiere had twenty percent less viewers than the season two premiere, and many critics worried that the producers were just making it up as they went along.  Damon Lindelof was aware of this, saying in an interview, "There was unease that they were making an investment in a show that is complicated, without any sense of where it is going to lead them, Fans have been saying, 'Are you making it up as you go along?'"  However, many critics have been happier with Season 3, because they claim there's been more action and some things are getting resolved. 
Additionally, the announcement of a definitive end to the series has allowed the writers to reveal answers at a steady pace, as opposed to "stalling for time".
Some fans have complained about the flash-forwards which where a major part of the narrative in season 4, criticizing that they were spoiling (part of) the outcome of the "present day" on-island narrative. Anyone who was shown as alive in the flash-forwards (the Oceanic 6, Ben) couldn't die in the present day narrative, thus taking away part of the suspense for the season.
Some fans don't like the Dharma Initiative narrative in season 5. Specifically, they complain that the once mysterious organization from seasons 2 and 3 was now being presented as a group of hippies sitting around and doing nothing of interest.
10 p.m. Timeslot (US Only)
"We literally saw a doubling between ['Lost' airing in] the 9 and 10 p.m. slot in TiVo-ing, more than double actually, I think that's a factor of it being on at 10; more people are DVR-ing it."-Stephen McPherson, ABC President 
Between the hiatus in Season 3 from "I Do" to "Not in Portland", ABC announced that it would move Lost from its usual 9 p.m. timeslot to a 10 p.m. timeslot in order to avoid a ratings battle from American Idol and Criminal Minds.  That was the third timeslot move that Lost had undergone in three years.  Many people were sceptical of this move, including Lost actor Naveen Andrews. In an interview, Andrews was quoted as saying, "I think they should make it sort of like what it was before, I liked it when it started a little bit earlier, because a lot of the audience are kids, aren't they?"  Reports claim that Stephen McPherson, ABC Entertainment president, claimed that he wants to move Lost to either an 8 or 9 p.m. timeslot. When McPherson was asked what timeslot he'd think would be ideal, he joked that it should be "Saturday morning, 7.30." 
Season One and Two Scheduling
During the first two seasons, there was criticism from some fans due to the amount of repeats broadcast between brand new episodes. To appease fans, the schedule was changed for Season 3, to reduce the amount of repeats.
Season Three Scheduling
"ABC's "Lost" has lost nearly half its live audience - more than 10 million people - from the days it was a sensation."-CNN.com 
In an effort to help Lost's ratings, in the 2006-07 television season, ABC aired six straight Lost episodes in a row in October and November 2006, then went on a thirteen week break, before coming back with sixteen straight episodes. Lost came back in February of 2007, only to find that many fans had left after the long wait.  Shows like "Heroes" and "Jericho" suffered similar problems.  By the end of the 2006-07 television season, Lost finished 17th in the series programming results.  Due to the criticisms of the hiatus, and to once again appease the fans, the shows producers and ABC changed the scheduling again, announcing a new format for the final three seasons of Lost.
Season Four, Five and Six Scheduling
Some people have complained about the new format of the next three seasons to come, which will air from February to May of each year for consecutive weeks, without repeats. ABC and the shows creators have been criticised for spreading 2 seasons worth of content (48 episodes) across three seasons. The shows creators have stated that having 16 episodes per season allows them to pace the show as they need to in order to tell their story.
The WGA strike affected the fourth season, resulting in the planned sixteen-episode season being cut short. Instead, the fourth season had thirteen episodes broken into 8 episodes, followed by a break, then 6 showing beginning April 2008. The series finale was a special two-hour episode, but is usually referred to as a single episode. The episodes that have been lost to the strike will instead be produced for seasons five and six, as the production is contracted to provide a specific number of episodes, not seasons.
Season 5 will have seventeen episodes. The first two episodes, along with a special recap episode will form the 3-hour season premiere on Wednesday January 21st, 2009. The remaining episodes will air for sixteen weeks straight on Wednesdays at the 8pm timeslot.
The show's last season, Season 6 will also have seventeen episodes, which are scheduled to air February-May 2010.
Other Outside the Show Criticisms
Sky One and Virgin Media (UK Only)
"Barring a last-minute deal, Virgin's 3.3 million subscribers will not be able to watch Lost, The Simpsons, 24 and other popular shows."-James Robinson, media correspondent 
For a while, BSkyB, the operators of Sky subscription based satellite television service as well as Sky One, UK broadcasters of Lost and Virgin Media, the major UK subscription based cable operator, had been debating their contract for carriage several of BSkyB's channels on the Virgin platform. Virgin Media claimed that BSkyB wanted to double the price of carrying Sky's basic channels package, which include Sky One, and BSkyB claimed that Virgin Media was trying to rip them off.  On March 1, 2007, Sky One was amongst several BSkyB channels dropped by Virgin Media, because of their inability to reach a new deal.  This meant that fans who wanted to watch Lost, along with other Sky shows, had to subscribe to Sky.  Both TV providers launched advertising campaigns against one another and talks have yet to resume.  Sky One is rumored to have paid £1 million an episode for the rights to air Lost in Britain. . Virgin Media have since purchased on-demand rights for Lost, allowing them to show episodes of Lost after Sky One has completed its broadcasts of the series. On November 4th a deal was signed for the channels to appear on Virgin Media, meaning that Lost is once again available to it's costumers.