I've had a couple of issues completing some missions in the Delta Voranis area. Unfortunately I've forgotten the exact names of the missions, but I can describe them:
The first one I had an issue with was a ground mission in an underground mine fighting Klingons. I got through the first group of Klingons and the mission said to take care of the reinforcements (apparently 3 teams). I meet the first team of reinforcements and get my butt kicked, but upon respawning the reinforcements disappeared. I went through tunnel after tunnel with no klingons (and yes, I explored every square inch).
There were graphical glitches as well: there were rectangular sections of the tunnel that appeared to be missing (they were all black, but I could walk on them) so it seems like the texture was not always mapping correctly. This frequently happened when a tunnel went into a "room" (larger tunnel) and when my avatar went in the room the av would disappear for a few seconds (except for the weapon) then the room would load and the avatar would reappear.
The other mission I had an issue with was one where the planet wanted medical supplies. I took the mission and went back to the starbase to buy the medical supplies, and came back to the planet. Before I could even hail the planet I noticed the mission log said 10/10 supplies delivered, but I hadn't delivered them yet and the hailing the planet indicated that it wasn't delivered yet. Pressing the "deliver" option did nothing. I think something is messed up with the mission progress steps on that mission, making it impossible to finish in the fashion I had to play it.
Same deal with medical supplies. Also, it's ridiculous that we have to spend game currency to complete a mission anyway. I'm level 11 and I got 2 medical supplies in all that time. I'd be president of the Federation before I found enough to finish the mission without buying it myself. Note: When a battleship Captain delivers supplies to, let's say Haiti... he doesn't pay for them out of his own pocket. You sillies!!!
it's not like money is hard to come by in this game. I haven't sold anything on auction, have all 3 ships, have bought stuff from auction, and still have 40k in reserve. I not only bought the supplies but also bought some of the other items up to 10 because this mission did forward to a second requirement for me before bugging. If I were to sell off everything in my bank I'd probably have another 20-25k also.
In regards to the topic, I agree it seems impossible to complete the delivery mission even if you have everything in inventory apparently.
As for the missing squads - this happens all the time even without the graphical errors. I've only had enough squads to fight one time out of 20 tries.