The first major issue is simply the lack of bandwidth. The physical layer operates at 3125 bytes per second, which just isn't enough for anything more than a single instrument with relatively sparse control data. MIDI devices can ostensibly be daisy-chained, but that's a really dumb thing to do because you get horrible timing problems. Back when we still used a lot of hardware synthesisers, it was the norm to have a large multi-port MIDI interface connected to your computer, providing one interface per instrument. That still doesn't solve your problems if you have a multitimbral module with lots of polyphony - if you start sending control channel messages, the timing of your note on/off messages will fall apart.
The second major issue is the lack of resolution. MIDI is an 8-bit standard, which is generally acceptable for velocity but grossly inadequate for most control channel messages. There are some pretty nasty workarounds being used to avoid zipper noise when you adjust a control parameter; this is most commonly an issue when sweeping a resonant filter. There are various hacks to send 14-bit control change messages, but they're non-standard aside from velocity and pitch bend.
MIDI is also built around the western scale, with no real accommodation for other tuning systems. We're forced to use the crude bodge of sending a note on message immediately followed by a pitch bend message; MIDI doesn't support per-note pitch bend, so you can't have polyphony and microtimbrality on the same channel. This is a fairly niche issue in the west, but it's a showstopper in a lot of other musical traditions.
OpenSoundControl addressed these issues and more besides, but it lacks widespread support because it was developed unilaterally rather than as an industry-wide collaboration. The spec is very powerful, but it just isn't very nice to work with. It's exciting to see that the MMA have a number of big players involved with the development of MIDI 2.0. We've been talking about fixing MIDI for a long time, but it seems like there's finally the traction to get a new standard widely adopted.