I wonder what show I was thinking of then.
Either DS9 where genetically enhanced humans were not allowed to join Starfleet or Babylon 5 where teleptaths were not allowed to join Earth Force.
I thought i vaguelly recall an episode (in season one perhaps?) where it was stated that Troi was just a civilian.
She's been an officer right from the start. In "Encounter at Farpoint" for example she wore a uniform and LtCmdr-pips.
My knowledge of naval terminology is a bit limited, but I was always under the impression that "Yeoman" wasn't a rank per se, but a positition
Actually, it's both, although it's not called rank but rate (rank is used for commissioned officers, rate for enlisted personnel). A Yeoman 1st class for example is a Petty Officer 1st class who works as Yeoman. A Senior Chief Yeoman is a Senior Chief Petty Officer who works as Yeoman, etc.
About Rand: She was a yeoman in TOS, a CPO in TMP, then we saw her as full Commander in TSFS but she was only credited as "woman in cafeteria", in TVH she appeared in an enlisted uniform and according to the script she was a Master Chief Petty Officer, next time we saw her (TUC) she was a Lt. JG, and then Voyager f*cked it up royally and showed her as Lt. Cmdr. Solution for that mess: Ignore TSFS and "Flashback".
O'Brien's even more messed up. We first saw him in "Encounter at Farpoint" with an Ensign pip, then in season 2 with full Lt. pips (he even got referred to as Lt. once by Riker). In "Family" he was referred to as "Chief Petty Officer" by Worf's father while still wearing full Lt. pips. His insignia was finally corrected in TNG's season six where he got one black pip. Then in one DS9 episode (I think it was "Past Prologue") Keiko mentions that he was promoted, but he was still wearing one black pip. In "Shadowplay" he referred to himself as "Senior Chief Specialist". Therefore I think that O'Brien was promoted from CPO to SCPO after his transfer from the E-D to DS9 and that the black pip is a generic insignia for CPOs, Senior Chiefs, and Master Chiefs.
There've been enlisted men in all shows and movies, just the complexity of their rate insignia varied from uniform to uniform. Best portrayal of enlisted men was beyound doubt in the TOS movies. Insignia were designed for every rate, they even wore different uniforms than commissioned officers and also the ratio between commissioned officers and enlisted personnel was much much better than in the shows. In TNG for example tons of officers were shown but only a handfull of enlisted men, but in TUC I counted approximately 10 officers aboard the Enterprise-A and all the other extras were enlisted.