It happens quite often that I cannot activate the Scavenger Trinket after having used and it has cooled down. I have no idea why as the icon shows it to be completely cooled down but when I select it and click like mad, nothing happens for a long time. If I switch to my weapon, kill some orks and wait some time it will work again.
How does the active ability of the scavenger trinket work
orcs-must-die-2
Related Solutions
I can't confirm this because I haven't played enough, but it seems like the scoring is pretty similar to OMD 1, so you might find this question useful. It links to a post on Robot Entertainments blog that has the point values for various combos and whatnot.
Aside from, getting high combo scores has been the best for points as far as I can tell. So combine a lot of different trap types with magic/attacks to get higher scores, each type of different damage source should increase your combo (ie, combo only increases once per type of trap that hits an enemy). I don't believe that coin forges actually help with your score, they just increase the amount of coins you have to spend during that level, so replace them with tar/fire traps to increase your combo multipliers.
To "spec" your character means to choose his/her powers. This is done in the spellbook.
To respec, simply hit the "refund skulls" button in the spellbook.
Best Answer
While the scavenger trinket is active, your character will have a blue-glow, and get an extra 1 gold every time you (or one of your traps) kill a unit.
The amount you earn for a kill is always shown breifly as a number displayed over the orc when you kill it; this number will go up by 1 when the scavenger trinket is active.
See also this question for information on how the ability stacks in coop.
The issues you are having are probably due to the trinket being on cooldown (shown in your inventory as being partially grayed-out), or not having enough mana to cast it (the blue bar at the upper-left of your screen).