So reported below, are existing bugs I've filed or commented on for a while. The double-mouse pointer, the crashes, the slow performance, etc.
I'm now encountering another problem consistantly.
I have Teleport set up on a MacMini w/ it's keyboard & trackpad. I allow it to control my laptop, when I have the laptop sitting next to it, which is usually

But whenever I take the laptop away, go work at a coffee shop for a day, suspend/reopen the laptop a few times, etc. When I come back and join the network, set everything up locally again.
Teleport refuses to recognize that the laptop is back on the network. I've waited and waited, and it won't do it.
When I load the prefs panel (the only fix I know of), I will see that the laptop is shown, but in RED. If I disable teleport, and re-enable it at that point, it starts working again.