The big one, considering it is intended as a field weapon, is that it needs constant cleaning to function properly. Field conditions are, in a word, nasty. You're not going to be in a clean-room, but somewhere dry, and hot, and with sand/dirt blowing everywhere; or in the hot, wet jungle with plants (and the attendant sap/pollen/crap) everywhere; or maybe in a swamp with water and decaying bio-mass getting in all the cracks... the whole M-16/M-4 platform is extremely fickle about any dirt/grime anywhere. {I've seen it act funny because of too much CLP and carbon from firing.}
This is all compounded by the difficulty of field-stripping the weapon for cleaning: it has a lot of parts, some that are pretty small and will easily get lost in the above-mentioned environs.
To illustrate allow me to present several rifles, filed-stripped.
This is the M-4, almost-field-stripped (the buffer & buffer spring are still inside the lower reciever):
The M-1:
Rather a lot of small parts, but a larger round & I've not heard of it being described as finicky in-general.
AK-47:
A few small parts, but it has a reputation for always firing (i.e. working in field conditions).
This is the PS-90, field-stripped:
No really small parts, compact, light, and has 50-round magazines.
The Mosin-Nagant:
"What's field-stripping?"