There's nothing cryptographically wrong with SSL (TLS and SSL are mostly synonyms in modern systems that disallow SSLv1 and SSLv2). SSL is actually an example of a cryptosystem done very right, which has survived and adapted to 15+ years of attacks. If you read the protocol, you will see lots of places that seem clunky, and almost all of them are countermeasures to older attacks.
The fact that a protocol with the same objectives as SSL that you wrote today would be far simpler and more straightforward than SSL is evidence of how important it is to use SSL, because you are not going to think of all the attacks that people like Paul Kocher thought of when they reviewed and modified the protocol.
The fact that a protocol with the same objectives as SSL that you wrote today would be far simpler and more straightforward than SSL is evidence of how important it is to use SSL, because you are not going to think of all the attacks that people like Paul Kocher thought of when they reviewed and modified the protocol.