Towards the end of a kitchen remodel I replaced all the switches with a nifty design with no visible screws. Unfortunately I misconnected a couple of them. Both are part of a 4 switch plate near the back door - both are "three ways" - ie. one switch there, one elsewhere for the same lights.

In both cases the switch I changed works the fixture it is meant to switch, but now the other switch for each (which wasn't touched) doesn't operate the fixture. One is the outdoor light in the breezeway - works fine from the kitchen but the switch in the garage won't turn it on, and if its on switching it from the garage just causes it to flicker once but doesn't turn it off.

What could I have done wrong?

 

You've inadvertently swapped a traveler with the incoming hot, or swapped a traveler with the wire to the luminaire.

The flicker is from the unchanged switch going from one traveler to another.

You'll need to identify where the hot lead is, where the travelers are, and where the feed to the luminaire is. One of the two three-way switches will have a hot, the other will feed the luminaire. In each case, the wire in question must be on the common terminal of the switch. The travelers go between the switches.