Like all games, StH4 has its problems, but I don't think that ruins it for the game. While it's very true that you're going to have far easier a time with a controller than a keyboard/mouse, overall, the game is very well put together. Piece by piece, here's what I think.
The music, like for all Sonic games, is very well done and feels very fitting. Every single stage sounds appropriate, from White Park Zone sounding very much like a snowy wonderland to Oil Desert Zone sounding like an intimidating desert factory. The music itself is composed fantastically, with nothing in it that would grate on the ears, and even the new power-up music doesn't sound too bad.
The controls and physics take some getting used to, especially if you haven't played a game with Sonic's acceleration need; thankfully, it's been improved somewhat from Episode 1, making it less bothersome. They can also be frustrating at times, but once you get over the slight learning curve, it never feels rage-inducing or overly frustrating. Annoying at times, yes, but at least here, it won't ever feel like the game is actively hating you and all you stand for. Sky Fortress' changed controls can take a bit to adapt to, especially if you're playing co-op, but other than that, failures mostly feel like skill or mistakes rather than bad controls.
The Zone desgins are wonderful as well. Each Zone gives a feel of some of the older games' Zones, but at the same time, they also have unique little twists or tricks that makes them feel like their own unique places as well. From White Park's snowy theme park feeling to Oil Desert's very industrialized setting, even if there aren't as many of them as in other games, they leave a mark.
The game is, despite some claims, not that much shorter than the other four games it emulates (Sonic 1, 2, 3, S&K). While there are only 4 normal Zones, every Zone has 3 Acts, plus a stand-alone "act" that's the boss of that Zone (not counting the final Zone). As an added bonus, you can replay any Special Zone you've beaten for fun, or to practice for harder ones.
Speaking of the Special Zone, the special stages from Sonic 2 make a return! And to add to the fun of the "friendly competition" of the ring gathering, the animation played when going between checkpoints is actually different depending on which character has the most rings. The stages, as usual, can be easy or hard depending on how good you are at picking up rings while dodging, but they definitely have the same feel as the old-school ones.
The co-op for the game can be either a blessing or a curse, depending on if you have someone to play with or not. The game feels very much like it was built specifically FOR two players to work together on it, which means if you do have two people, you can do a lot you wouldn't get to do or pull off some neat tricks. At the same time, if you're playing alone, it can sometimes be a little frustrating or difficult precisely because of the build intending two people.
All in all, it's definitely not a perfect game by any means... but it's a game that those who enjoy that style of gameplay should, in my opinion, pick up if they can, regardless of whether they're a Sonic fan or not. Those who are fans of the old-style Sonic, however, will definitely find even more enjoyment in it with all the throwbacks. However, I would DEFINITELY reccomend a controller if at all possible.
SEGA managed to make something that felt both old-school and unique with Sonic 4 Episode 2... and how many games can claim that?