Telepathy: Telepathy (or rather, techlepathy) is a somewhat limited faculty, as described under Psychic Powers. Being essentially a way to transmit neural gestalt information over WiFi, it is an excellent messaging system, complete with the ability to transmit images, emotions, information constructs, and other non-verbal information, and communicate broadcast/narrowcast, local/distant, private/conference, etc., etc., and even to synch up well enough to form a conflux (see: Mental Fusion).
It doesn’t, however, let you overhear people’s thoughts (unless they’re sloppy and accidentally broadcasting, which does sometimes happen), go in and pull thoughts out of their heads (you want a SQUID for that, or a mind-state reader of one sort or another), control minds (although you can inject the same memes as you can over any communication channel), or enable the rest of the assorted magical aids and attachments (dream travel, astral projection, and so on and so forth). It’s also, being EM based, limited to the speed of light.
Since it’s harder to fake all the sidebands, a telepath can sometimes be something of a Living Lie Detector, but reliability in this role still isn’t great, and you are almost certainly better off with a regular mechanical alethiometer (which uses a SQUID).
Goggles Do Something Unusual: Since medical technology has long since adapted to the point of being able to fix just about any eye problem imaginable, any time you see glasses on someone’s face – and there are periods of history where you will see this quite a lot – you might suspect that they’re there to serve some other function.
You would be right. Usually, that function’s just acting as I/O for a wearable or other PAD devices, which means that they combine a head-up display with stereo cameras (these enable augmented reality, freeze-frame, enhance and rewind, among other things; and even when neural laces replaced wearables, a lot of people kept them around as a popular way to lifelog), microphones, eye tracking, and ability to participate in a wireless PAD (such that they can communicate with your wearable, but also with any other networked devices you might be carrying, which is probably all of them; your gun, for example, certainly uses them as a scope) including a gateway to the greater network and all its facilities.
Of course, technological ingenuity being what it is, there could be anything from a T-ray scanner through a general-EM reader to a full SQUID in there, sensorily speaking, or a couple of nanomissiles or a few BIPS of processing power concealed in the frame. It’s really best not to assume what the chap with the glasses might or might not be capable of seeing.
Psychic Powers: Of course, there is absolutely no such thing as psychic powers. Don’t exist. No place in a rationally organized universe, like any relatively firm-to-hard SF universe. Can’t seriously believe otherwise.
But that said…
Telepathy/Empathy: Do you believe in wireless networking? Evidently the Precursors did, and they really hated waiting while runners were sent or shouting was done, because they built this one right in to the brains of their favored manufactured race. If you want to detect telepathy, you’ll find it in those weird screebly neural-gestalt signals hanging about in the high microwave part of the EM spectrum.
Precognition: Do you believe in clionomy? (On the large scale, the gentle art of computing statistical predictions concerning the future of organizations and societies.) And very advanced predictive algorithms? (Because with a computer in your head and advanced enough body-reading, simulation and prediction software – and maybe a little SQUID use – you can read people and predict their future actions in a downright spooky manner. Especially when done in combat.)
Psychokinesis: Do you believe in implanted vector-control effectors? Another fun now-reverse-engineered Precursor leftover tech, these tiny nervous-system-integrated nanopicosomes are all you need to toss gravomagnetics around, fetch yourself drinks without standing up, indulge in wuxia wire-fu, and kill people with your brain to your heart’s content.
All available in stores for the usual enhancement prices, should you be unlucky enough not to be born with them built in…