I also like "If you think you understand quantum mechanics, you don't understand quantum mechanics" which is supposedly also from Feynman.
Quantum _mechanics_ cannot be understood, it is full of paradoxes. It contradicts classical EM and special relativity, among other things. A toy theory that was an important step to what came later.
Feynman's own QED is a part of QFT, but this is no longer quantum mechanics. Special relativity and quantum physics are reconciled since then. Now, we only need to reconcile GR and QFT, but this leap was so far beyond our attempts to scale it. Yet, QED/QFT/SM can be "understood" as there are fewer obvious paradoxes that plagued QM.
I think it's one of those famous quotes that was never said. The one I quoted was what he apparently said.