Annoying Video-Game Helper: Seeing the same types of hints/restrictions for the same types of special blocks/switches every single time you pass in front of them, especially when trying to solve a completely different puzzle in the same area, gets very irksome.
Broken Base: Since LEGO Batman 2: DC Super Heroes all the games have used voice acting. Some fans like the voice acting because they feel it gives the storylines of the games more depth and makes for more joke opportunities, while you have others who think it makes the humor more cringey and annoying.
Invincibility is featured in all games as a power-up to unlock. Granted the games are already simple, but some of the in-game cheats provide effects that are God Mode incarnate. EspeciallyStar Wars: The Complete Saga, but that game has thirty six stages to search compared to the others so it makes perfect sense. LEGO Marvel Super Heroes is thus far the only game to not include it as a cheat - Emma Frost's diamond form is invulnerable, however.
The Stud Multipliers, especially as they stack (except in the DS versions, save Rock Band and Indiana Jones 2, where you probably have gotten everything anyway). How does a multiplier of 3840 (2x4x6x8x10) sound?
Growing the Beard: Developer Traveller's Tales was not held in high regard until LEGO Star Wars. The franchise is viewed to have done this since then as well, although nobody is sure as to when specifically.
Hilarious in Hindsight: One of the songs in LEGO Rock Band was the theme of Ghostbusters. Five years later, and LEGO has released an (albeit online-exclusive) set featuring the main team and the Ecto-1.
It's the Same, Now It Sucks!: Easily the most common complaint about the series - the games are in essence Strictly Formula with only minor differences. Even many LEGO fans aren't interested in the later games for this very reason.
Nausea Fuel: The "Dynamic" split-screen, when you have one co-op character flying around and another standing still trying to do an aiming task; or even worse, when both are in flight. In different directions. It gets difficult to focus or not get dizzy.
Numerous features introduced in the LEGO Star Wars sequels actually made their debut in the Gameboy Advance version of the first game. For example, the Jedi Mind Trick, Lightsaber Throw, and invincibility power-up, which would not be introduced to the console versions until The Original Trilogy, The Clone Wars, and The Complete Saga, respectively.
Zig-Zagged with the voice acting, as a lot of fans reacted in over-the-top ways when they found out LEGO Batman 2 was going to be the so-called "first" LEGO game with it. While it was the first in this series, itwasdonecountlessothertimesinthepast. Heck, some people aren't even aware LEGO games before these even existed. To make matters worse, the box itself for the console versions actually claims this is the first LEGO game to have voices, period.
When LEGO Star Wars was first released in 2005 many people were baffled by the concept, some even thought it was a joke. Apparently they were unaware that LEGO had been making Star Wars sets since 1999. It wasn't LEGO's first licensed video game either. They had already made two based on their Harry Potter line.
Periphery Demographic: The games are popular with kids, though they're also popular with adult fans of LEGO and the franchises they're based upon, due to the copious amounts of tongue-in-cheek references and nods to the original work. LEGO Marvel Superheroes and LEGO Batman 3 seem to be running with it, due to featuring many obscure or less prominent characters in the game (even if not necessarily plot-relevant), and numerous references to popular stories and concepts.
Scrappy Mechanic: Free Mode tends to select characters to play that suit the level's many secrets, but sometimes they don't choose characters with enough abilities to do the level's challenges, forcing either a level replay (though this has been fixed since LEGO Pirates of the Caribbean) or selecting a character manually from the select screen, which sometimes slows down the pacing of the level due to the game loading up the character that isn't in the rotation of characters selected for the level.
Jumping puzzles can get incredibly tedious with the number of attempts it takes to get them right, especially in earlier games (and some levels in the later games, though it's averted in the hubs now) where you couldn't select the camera angle. The animation is good, but not good enough to always give the requisite depth to gauge where your character is in relation to their environment and the jump targets. Depending on which console you're using, the button combinations required can make this even trickier, especially if you're playing on the Wii and have to target exactly using the movement of the controller at the same time as getting the combo right. Later games, beginning with LEGO Jurassic World, seem to have finally addressed this properly by having the characters lock on to their next jump target automatically, leaving the player just to worry about the timing.