iPhone 4S text message annoyance
I have encountered this issue since the betas of 9.0 and can confirm it up to 9.0.2.

The reason for the appearance of this issue is that the iPhone thinks you are trying to record a message. This occurs whenever the proximity sensor thinks that you have put your phone to your ear or otherwise been fooled into thinking so.

This feature works fine with iMessages, but SMS obviously does not support sending voice messages. Whatever the reason, it gets triggered but the software does not know how to handle it, leaving it in the inconsistent state.

A temporary solution is to quit the Messages app with the Multitasking switcher, or trigger a voice message in an iMessage conversation and cancel (which interestingly prevents the issue from reoccurring while the Messages app remains in memory).

The ultimate solution will have to come from Apple in a bug fix.