I never had a problem with text messages on my iPhone 4, but have had several since upgrading to the 5, especially in the last couple of months:
1) Recently, I received what was obviously a reply to a group message and couldn't figure out what it was about. I assumed it was a response to a message thread I had deleted earlier in the week and didn't give it another thought. However, later that evening my daughter mentioned several texts she had sent me earlier that I never received. I rebooted the phone and suddenly all kinds of texts and iMessages came through...including the rest of the conversation that the first message related to.
2) Last Friday, I arrived home from work and immediately received multiple message alerts. Turns out several family members had been having a group conversation to plan a family event later in the weekend. I didn't receive any of the messages until hours later.
3) I haven't been able to send a group message for quite some time now. The message will start to send, then gets hung up and finally I get a "message failed" alert. I can respond to group messages, but cannot initiate them.
4) I haven't been able to send a photo via text messaging for quite some time. Same thing as with group messaging, the send process starts, then fails. I can email photos, and can upload to FaceBook and Instagram, but can't send via text or iMessage
5) Not message-related, but lately I've been getting voice mail notifications when the phone never rang to begin with (no missed call either) and a few people have told me they called but the call never came through.
6) Battery life has significantly decreased since installing iOS6. In the past, I could charge my phone overnight and use it often, including apps such as FaceBook, web, messaging, email, and would still have enough battery life to go through the next night if necessary. Now it hardly holds out until that night.
Never had any of these problems with my iPhone 4, and didn't initially with the 5. Any suggestions, or could this be an equipment issue?