In short:
telegram in secure chats (http://core.telegram.org/api/end-to-end) was using modified version of Diffie-Hellman algorithm:
key = (pow(g_b, a) mod dh_prime) xor nonce
(original: key = pow(g_b, a) mod dh_prime)
That custom 'nonce' is derived from server and in theory server can send a specially formed nonce which will lead to known client keys ("bookmark"). It means that server as MITM can read all needed chats by request..
Authors of Telegram agreed that it is a big hole and their algorithm needs modification. User, who found the issue will get a prize (not 200,000$, but good enough).