I just installed the pickups in an old LP style guitar I was working on and the only thing I get out is a hum with no sound from the pickups... All the wires are new, pickups (humbuckers) are used but measure at the correct resistance, input jack is new.

The pots and the switch are stock, so they are ~25 years old.. I checked the pots and they seem to be working fine according to my ohmmeter.

I grounded the pots to the back of the tremolo.

I used a wiring diagram for 2-wire humbuckers from seymour duncan (the actual ones I have are out of a Dean)

Where should I look for some trouble spots?

Well how did wiring go? Were you able to get it exactly like the diagram, or did you have any issues/differences?
Here is another diagram
Little bit different than yours.

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Wired it exactly like the diagram. The other diagram you posted needs 4 wires, these pickups only have two. It has a bare wire and a white wire, I put bare to ground and white to the pots.

The only issue is that I had to solder on an extra length of wire to the caps to allow them to reach between the pots, but I don't think that would be an issue?