This is a somewhat minor quibble, but the flavor text of Precognition refers to seeing the future days in advance (and the summary on the little table refers to it as a seeing-the-future power) but the power itself is only good for one round, which I'd interpret as meaning the vision only refers to the immediate future (After all, why would knowing that the city will explode in three days help you dodge a bullet now?)

In a similar vein, the Prescience power gives a bonus to WS and BS, which I think most players would interpret to mean their Prescience is limited to "Oh! He's about to jump up! Shoot now, shoot now!" The GM sidebar on divination, however, seems to assume that players and GMs might think it reveals useful information about the actual future.

Does anyone else think these powers need clarification?

I agree with you here. I think they either need a more appropriate explanation or a reworked effect that matches the given description. The psychic powers in Beta 2.0 are copy-pasted directly from Only War, which unsurprisingly doesn't involve much investigation. Personally, I would prefer that most Divination powers provide non-combat, investigative benefits. Maybe one or two "combat precognition" powers would also be appropriate just to give the discipline some combat utility, but I feel that most of the powers should involve auguries, scrying, dowsing, sensing emotional resonance, and reading past/future events.

The way I would interpret this as a GM would be to reveal a small snippet of something the bad guys are going to do in the future. Of course I wouldn't reveal too much and leave it as more of a question that the PCs need to solve but should give them a few leads.

I don't think there's any doubt that the flowchart description for Precog is just wrong - "days" vs. ~4-5 seconds.

But on the broader subject, I would agree with Covered in Weasels that I'd like to see Divination have more focus in non-combat investigative benefits, as he puts it. I will say, however, that I wouldn't mind that these true divining powers be expensive - as I think the fluff supports that true diviners are on the rare side.

Specifically, from DH1 I miss Psychometry, Personal Augury & Soul Sight (pg 172/173 in DH1 Core). Something I really liked about these powers, in particular, was the structure and support they gave to the GM to implement them. All three come with their own extensive explanation and their own table for implementation. Divining powers can be challenging on the GM and I think a good built-in structure like that is necessary.