I've changed the part in the FAQ that seems to be one of major sources of this controversy, so that it no longer reads "built from scratch". This was poorly applied marketing language — we do use time-tested security algorithms. Even though Telegram doesn't uses MTProto instead of HTTPS due to mobile speed and trust issues.
AES in what mode? IGE? Why are you using an authenticated cipher mode from the 1970s that predates every modern AEAD construction?
DH with what group? How do you authenticate the exchange? How does forward secrecy work?
Saying "we didn't roll our own: we use RSA, AES, and DH" is extremely worrying; it suggests that you're not aware of where the complexity in a cryptosystem lives. Anybody on HN can write the trivial code to ask the JCE for an RSA or an AES. You have to do better.