Could there be any issues having both POE and AC power attached to a WAP? I'm curious because I found a few WAPs that had both...wondering if I should pull AC or just let it ride?
The Powered Device should recognize it has "local power" and not request PoE power. This assumes that you're talking about 802.3af compliant devices (sometimes called "active" devices) and not "passive" power injectors and their associated devices (they just throw voltage "out there" without regard for necessity, destination, or compatibility).
What you should do about this depends on your environment. If your PoE switches are heavily loaded, a few devices operating off local power is likely a good idea. Same for devices that require more power than your switch can provide.
For devices that use passive power injectors, they should absolutely not have two sources of power going to them. This could create feedback loops, ground loops, and all kinds of potential for misbehaving or fried equipment.
The PoE spec says that a device that can accept both PoE and power from another source must isolate the power sources so as not to send power back through the Ethernet connector. So if you're using reputable stuff, then your network gear should be OK.
That being said, the spec do not address what the device should do when it has power via PoE and another source. You will have to consult your product documentation as to the behavior of your device when it has multiple power sources available.