I don't know if there are "trap doors" so to speak about memorizing - but there are some things to watch out for.
The first is that you are right - when you are getting familiar with a piece, your memory is starting to firm up and sight reading becomes less important. This brings up the notion of the different kinds of memory involved when we play piano. Do a search on Piano Street on muscle memory to get a lot of discussions of this.
In a nutshell, we remember pieces (or bits of pieces at times) in different ways. One way is through the muscles - your fingers seem to head to the keys before you are aware of them doing it - this is muscle memory. Another way is visual - we remember how the notes look on the page or the pattern of the keys on the keyboard as we play the piece. A third way is musical or intellectual - this comes with musical maturity. In this memory, we remember the musical structures of the piece, not just the notes. These could be the harmonic progressions, or repetitive patterns. And finally (for my memory anyway!) there is audio memory - we remember how the piece sounds and the brain can direct the fingers that way.
All of these can be used when playing the piano - the key is not to depend on only one way of memorizing because then we are liable to get lost. For instance if we only relied on visual memory and use different fingerings and hand motions, then we don't get the advantages of muscle memory. And vice-versa, if we only have muscle memory then we can quickly lose our place if we don't have a concept of the musical structure of the piece.