One MacRumors forum user has posted his story of how he resolved his iPhone 4's antenna/signal issue. The story basically says that while at the Genius Bar at a local Apple Store, attempting to investigate another technical issue with his iPhone 4, the user's SIM card was removed for a period of time and then placed back in. He found that reception improved and the antenna issue was nearly gone:

I went on my merry way, but realized something now. No matter what position I held my iPhone 4 in, the signal never decreased. I held it the many ways I know the signal issue pops and nothing. No bar loss, no signal loss, no call drop. NOTHING. So there you have it.

I am theorizing that moving the SIM card had something to do with the signal issue, because the only thing I have done to my iPhone 4 differently is take out and reinsert the SIM card. Other than that no other changes to it. No setting change, no software change no nothing. Just reinsertion of the SIM card.

He later asked people try attempt to do the same thing, to see if it would help anyone else, and it was then when people theorized that the issue could be caused by the SIM card contact with the SIM tray might be loose.

Users then tried many different things to their SIM card/SIM tray, such as placing electric tape on the card, or even cutting the other side of the card to make it fit better. However, the responses from the users who tried this have been mixed, with some reporting that their signal issues have been completely resolved, and others reporting that they still have the same reception issue. Here is the response from a user who claims his reception issues are gone.

I just tried this. My sim contacts were under the edge of the tray too. I cut a piece of electrical tape to exactly cover only where the gold contacts of the sim touched the tray. I went back to the exact location in my house where I had 1 signal bar. I now have 3 signal bars. Unreal, I can't believe this did anything. Tested before and after with a bumper on the phone. I'll keep an eye on the performance outside the house tomorrow. I don't want to jump to conclusions that this helped my iPhone reception without more data. Looks promising so far though!

Here's an interesting note/thought - if the SIM card is truly the cause of the antenna issue, when a user would get a replacement iPhone 4, the SIM card would be transferred over to the new phone, meaning nothing would change.

For more details, you can take a look at the full discussion thread here.