The concept of taking various licensed LEGO properties and throwing them together is great. Some of the properties, like Portal and Doctor Who, have been treated with evident love by the game designers. The controls are less convoluted than some recent LEGO games (LEGO The Hobbit was especially overloaded).
But for all the fun in the idea, there's some big negatives.
First of all, there's the cost. The entry cost is $99, and that just lets you play part of the game. If you want to get all of the gold bricks and other extras, you're going to need to by expansion sets—and a lot of them. In previous LEGO games, you unlocked characters by finding character tokens; in Dimensions, you unlock characters by buying real-world packs with real money. Even if you don't want to collect all the characters, but you just want to access all the hidden areas, Dimensions will cost you several hundred dollars. Many things are hidden behind things that require one specific expansion character to unlock. While the various packs aren't priced particularly high compared to non-game LEGO building sets with similar parts counts, the fact that you will need so many sets just to get 100% on the basic storyline means that this game requires a substantial financial investment.
The game's story mode is short compared to recent LEGO games, although the "adventure worlds" make up for that somewhat. Likewise, the "level packs" that add new story levels are very brief.
As for the controls, TT has traded complex menus on-screen for the toy pad. In many places, you need to use the pad and your characters as controls, moving them to different slots on the pad. That adds a new kind of control complexity. You can't just sit down and play the game; you need to have your toy pad within reach. It needs to be on a non-metallic surface, away from any sources of RF interference. It needs to be within reach of your console; it uses a long USB cord to connect. It needs to be on a relatively level, stable surface. And you'll need to have room nearby for your collection of characters and vehicles so you can swap them in and out. The need to constantly shift attention to the toy pad draws you out of the game, especially when you find you need to remove characters from play to make room to swap others from section to section. Like the Wii U's second-screen, it's an idea that sounds good in the abstract but isn't very fun in reality. (At least in the 1.02 patch, some character abilities can be activated with a button press instead of requiring toy pad movement.)
The game also suffers from TT Games' long-standing LEGO game-engine bugs. After a decade of LEGO games, TT still hasn't fixed problems like characters getting stuck in places with no way out, or the game occasionally locking up for no apparent reason. (The Doctor Who level pack has a nasty bug where having the artifact-detector red brick enabled causes the game to crash reliably on multiple platforms, making the level unplayable until you disable the brick.) It also adds some new glitches, such as places where your character can fall through the world and die in the offstage area that you should never see... and then respawn offstage right above where you died, creating an infinite loop of falling, dying (and losing studs), and respawning that you can't escape without quitting the game (and losing progress). For a game that will cost several hundred dollars to complete, there's no excuse for not delivering a stable game without ancient bugs. It can be done—the Wii U-only LEGO City Undercover was virtually free of the typical TT Games LEGO bugs—but it wasn't done for Dimensions. If the game were free of these long-standing bugs—heck, if it were even free of bugs that should have been caught with minimal pre-release playtesting—it would be a four-star game. As it is, only the charm of the writing and the concept keep it from being a two-star game.
The various properties in Dimensions receive varying amounts of care. For example, the starter set characters all have fairly extensive dialogue from the original actors. The Doctor Who, Portal, and LEGO Movie characters also receive extensive voice acting from the original actors, including minor characters. The Lord of the Rings characters receive the same over-used movie sound bites as the standalone games, which are sometimes even appropriate to the situation. The Ghostbusters levels available so far seem to rely exclusively on movie sound clips. The Simpsons properties are missing dialogue for many of the characters.
If you have a lot of disposable income and a high tolerance for replaying levels due to game-ending glitches, LEGO Dimensions has a lot of fun in the way it lampoons its subjects and mashes them together. If spending $300 to $800 to play a buggy LEGO game doesn't appeal to you, you might want to skip it and just watch gameplay clips on YouTube.