If you were to hash a user\'s password prior to sending it across the line and leaving it in plain-text in memory, would this improve the security of the application?
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Hashing on the client side opens up another huge hole: you may expose the hashing algorithm. You don't say whether this is web-based (client=JavaScript) or thick-client, but you're giving them more information. Given the channel is secure, you don't have to worry about the clear text password being sniffed.
Besides, if your hashing algorithm requires a salt, you would be exposing your salt, which means if they ever got access to the database, they would be able to decrypt every password.