(Warning: shameless self-promotion ahead) In my lengthy fanfic "Return to the Realm", I have Uni tell the gang that unicorns communicate telepathically, mind to mind. I believe that there's evidence for this. "Valley of the Unicorns" opens with the wolves of Kelek attacking a unicorn named Silvermane. We suddenly cut to Uni reacting in terror, but nobody knows what terrified her; they could neither see nor hear what was happening to Silvermane. I think it isn't too much of a stretch that Silvermane sent out a telepathic SOS to any other unicorns nearby; Uni just happened to be the only one.

So why didn't Uni communicate telepathically with the kids, and why was she such a noisy little bugger? I think the two questions go hand in hand. We never know how Uni hooked up with the kids in the first place, but we do know she's very young. She could have been separated from the rest of her kind before she understood her telepathic powers or knew how to use them. ("Valley of the Unicorns" already established that she didn't know unicorns could teleport over short distances.) By spending a lot of time around humans, she would have noticed that they are not telepathic, and that they can only communicate through talking. The equine and human vocal mechanisms are quite different, of course, but, like a young child, she would try to copy what everyone around her was doing. Hence her persistence in trying to communicate verbally--generally a failure.

There was one exception, however. In "P-R-E-S-T-O Spells Disaster", Presto ends up hanging from a high branch, unable to cast a spell to save himself. Uni, however, takes the hat in her mouth, waves it around and squeaks out her usual gibberish. It results, however, in a flying carpet that carries Presto to safety. He had to have mixed feelings about that one; when a mushmouthed unicorn with a hat in its teeth still managed to cast a better spell than he could--

I've already alluded to another unicorn power mentioned in the series: teleportation. They can send themselves short distances, but only once per day. This is the only way we know that "Prison Without Walls" happened after "Valley of the Unicorns"; by that time, Bobby knew enough to tell Uni to teleport. (Quite a few fans have complained about the lack of internal continuity in the series. This sequence is literally the only clue we have toward putting the series in some kind of chronological order; literally nothing in the series relates to anything else.)

Basically, Uni is a cross between a pet and a four-year-old. She gets underfoot at inopportune moments and sometimes talks too much. Still, she's affectionate (especially toward Bobby) and manages to befriend a couple of other critters (notably Martha's pet Wiccan and Terry's dog Freddie). She suspects Karina's intentions before Sheila does, and sees through Varla's illusion to Venger's real identity in "The Last Illusion". She uses her alicorn to cut the web and send Loki to her death in "Hall of Bones". She fetches Sir John when the gang has been captured by giant snails in "Eye of the Beholder". She creates a diversion during "In Search of the Dungeon Master" that distracted the Orc guards. In short, she was limited, but did what she could, and the group was better off for it.