The "blink and you'll miss the battles" multiplayer speed definitely hurts the experience for me. I have a lot of trouble controlling the units in any meaningful way in fights because of it.
I haven't tried HotS multiplayer yet. I have tried some games against the computer. They have a new game mode that uses a matchmaking sort of concept to put you against computer opponents of your skill level. From memory, it's a bit like their old coop vs AI system except it sets the difficulty for you. You can still play custom games against the computer if you want instead using the custom game interface. I kinda like the new thing, but the computer still doesn't seem to know how to wall, which is sort of bad for its early-game survivability (can you say "ling go"?).
I enjoy the multiplayer (or non-campaign, say) modes as the price of admission to understand the pro games well. They help me learn the units to an intuitive level that it's hard to pick up from blurry streams.
ETA: oh, and I wanted to add the new training modes and the AI matchmaking system are in Wings of Liberty after the 2.0.4 patch, so you can just check them out there if you want. I thought the training modes were really nice - three modes of increasing complexity with restrictions on what you can build and continual advice from the computer.