I'm a Red Alert kind of person. I loved RA2 and Yuri's Revenge, but RA3... that had some strong points, and a ton of weak ones, some of which are detailed below:
1) RA3 didn't have sub-factions like RA2. I like adapting my strategies to what special units my opponents have. In RA2 I always go Great Britain or Iraq if I'm not using Yuri.
2) The implementation and use of different camera angles. I didn't need them when the standard isometric view of RA2 was perfectly good enough.
3) Half-disguised Spies. The RA2 Spy is much more awesome than the RA3 one, on account of the fact that he actually turns into a copy of the unit instead of projecting some sort of holo-field. The Mirage Tank, Sudden Transport and any others I may have missed do the same thing. On the subject of the Mirage Tank...
4) The Allied Mirage Tank was a failure. It tried to be a hybrid of RA2's namesake and the Prism Tank, and turned out to be less effective in combat than either of the two, in my experience.
5) As Plinglebob mentioned, the pseudo co-op. I don't like sharing my bases with an AI.
6) The way each faction builds its buildings. I much preferred the simple route RA2 took, of prefabricating the structures in the menu, then deploying them from the Construction Yard. The individual tech-trees are alright, but the building processes just annoyed me. As a side note, build zones are something from Dawn of War. They shouldn't be in Red Alert.
7) (Here comes the big one.) The obviously designed "sex appeal" of some characters, most notably the commandos and assistants (Lieutenant Eva and her Soviet/Empire counterparts). I sigh in disappointment at the changes to Agent Tanya. She has a sense of badassery to her - and decent hair and voice responses - in RA2, but in RA3 she was a blonde with too much make-up on. Don't even get me started on the other commandos. Natasha is the best in terms of gameplay, but design of all three was a huge letdown for me. Especially since Yuriko was too short-ranged to be effective.
Those are all that I can think of right now. However, I thought that the majority of the acting in the cinematics was good. Tim Curry in particular was brilliant, in my opinion.