Shaft seems fine, if a bit weak. I like it.
Panniers has me a bit confused. If you use the reaction effect, do you get +1 card? I'm also not sure why it returns a card rather than simply trashing it. That's a valid choice, I'm just not sure what it adds really. I think the on-play effect could be buffed.
Weaver seems rather strong. I'm sure Weaver/BM could be beaten sometimes, especially with that sifting effect, but I worry that Weaver/BM might too often be the dominating strategy, and not interactive enough with the rest of the kingdom. You should try it of course. But I think it should be made less extreme.
Law, by contrast seems too weak. For comparison, consider Catapult. Catapult not only gives $1, but also provides a benefit upon trashing copper.
Midway seems pretty interesting, although not strong. The reordering ability seems like a fairly important part of what makes it good.
Privateer, well here's a card that I think would clearly be more interesting without +Buy. For one thing, you could make it cheaper. And you'd find yourself in a variety of situations depending on the rest of the kingdom. If the +Buy is on treasure, then you have that nice bit of synergy. On the other hand, if the +Buy is on an action, you have to play the action before your buy phase. So maybe you have a mix of Privateer and traditional draw, or else you hope to have the +Buy in your starting hand, or maybe you just do without +Buy.
I have issues with Alderman. It seems kind of slow to play with, and without good reason. Most often, you reveal at least one action, and now Alderman is an expensive village, hooray. Maybe you reveal a victory card and can play your Mill, making Alderman a double village. But so what? I'm not sure what Alderman is really for, but honestly it sounds weaker and less interesting than a vanilla card that just says "+1 card, +3 actions".
I also have issues with Prowler. Mainly it's a glorified woodcutter. Or if you're buying treasure, and have extra buys, it's a glorified treasure. I think you could do more with a simpler card, e.g. an action/treasure that only gives +Buy if you play it in your action phase.