I'd say starships are easy. They have warp engines, after all - and those supposedly expend fantastic energies to produce FTL effects. It only stands to reason that they leak FTL radiation in all directions, radiation that can be easily and virtually immediately be picked up by passive sensors lightyears away.
Even starships that aren't moving at warp might emit FTL radiation from their idled engines. Their navigational deflectors might also glow like beacons, and they'd likewise employ FTL emissions to reach ahead of the ship. Most of the combat systems are likely to glow as well. And cloaks can only do so much to contain the glowing.
Now, observing realtime events on a distant planet is probably more difficult, because most planets don't have warp engines. Then again, our heroes very seldom do observe realtime events on distant planets - they merely observe things that might well be several decades out of date (and thus observable at lightspeed), such as the planet's climate, atmospheric chemistry, state of industrialization and whatnot.
Probably some sort of a FTL radar could also exist, though. It would send FTL energies outward and listen to the echoes or secondary emissions or whatnot. And while realspace is vast and distant targets thus impossibly small, subspace might be a different matter.
Timo Saloniemi