If you do not salt your Password, you're suspect to Rainbow Table attacks (precompiled Dictionaries that have valid inputs for a given hash)
The other developer should stop talking about security if you're storing passwords in plaintext and start reading about security.
Collisions are possible, but not a big problem for password apps usually (they are mainly a problem in areas where hashes are used as a way to verify the integrity of files).
So: Salt your passwords (by adding the Salt to the right side of the password*) and use a good hashing algorhithm like SHA-1 or preferably SHA-256 or SHA-512.
PS: A bit more detail about Hashes here.
*i'm a bit unsure whether or not the Salt should to to the beginning or to the end of the string. The problem is that if you have a collisions (two inputs with the same hash), adding the Salt to the "wrong" side will not change the resulting hash. In any way, you won't have big problems with Rainbow Tables, only with collisions