I have to concur that in general, Rolemaster's initiative/round sequence is possibly the bit that could stand the most improvement. Being a primarily a wargamer who roleplays, I've learnt that the game sequence is pretty much the most important factor in a set of combat rules. One of D&D 3.x's cleverest inventions was it's round sequence, which works quie nicely. I've been playing Rolemaster since about 1990 or so, and I note that a new initiative/round sequences come up with great frequency, and I've tried several of them; none of them have hugely satisfactory. (Considering RMC's version is but the latest of them - which I plan to try out at my next game - I'm clearly not the only one).
Now, I'll grant you I'm not sure myself what the best way of working it is; I think the new RMC system is slightly more elegant than the RMFRP/SM:P system we've been using for the past few years. (I found that out of my group of about eight players, only myself and one other player were really crunching the numbers between Snap, Normal and Deliberate actions and the three phases did slow combat down quite a bit. Granted, sci-fi with lots of guns - including pistol dual-wielders didn't help!) Action declarations are cumbersome too.
At my christmas game, I'm basically planning on using the RMC system, but with my own initative (which is basically QU bonus/5+2D10) and making round seqeunce roughly cyclic like D&D 3.x's is. Rather than have action declarations, I might have some, but primarily I'll ask the PCs what they want to do on their action on their initiative count and resolve it immediate;y (or not, if it's a long action.) I'll see how that goes...