Update: Now that Grand Theft Auto V is actually out, players are testing the previously suggested USB flash drive alternative to an HDD install. Turns out that solution actually works, as confirmed by many, including Neo user m2caldwell.
If you'd rather not run the play disc through the Xbox 360 DVD drive (Who wants that?) but aren't keen on experiencing the performance problems of an HDD install, simply use a USB drive instead. Installing the play disc/disc two to a USB flash drive and running it from there reportedly eliminates those pesky pop-in textures and missing objects, while being a whole lot quieter than the 360's DVD drive.
Original (9/16): If you plan to get the most out of your Grand Theft Auto V experience on Xbox 360, don't install the second disc to HDD. At least, that's what Rockstar is suggesting, and we now know why. Seems that installing the "play" disc (that's disc two) to your 360 hard drive creates a good chunk of in-game issues, from texture pop-ins to missing objections.
On Rockstar's official Twitter, in a tweet that suggests not installing the play disc for anyone wanting that optimal performance. Basically, you'll have to install disco one, but run disc two directly from the DVD drive.
The tech analysis folks over at Digital Foundry decided to try that out anyway, since no one really knew why Rockstar made this suggestion. Well, they figured it out, but during their numerous tests, the team also figured out that you can install the play/second disc to a USB flash drive, which leaves you the HDD space for that mandatory (disc one) install, if you need it.
A video comparison does give us a good idea of the performance issues caused by installing the play disc to HDD, and the results are actually pretty jarring. The problem here is that installing disc two, which takes up an additional 7.8GB of storage, hinders the game's ability to stream texture data, resulting in what you'll see below.
No word yet on whether the PlayStation 3 and PSN versions will suffer any similar issues. Grand Theft Auto V comes out tomorrow, September 17. Remember that if you pre-ordered the game through the PlayStation Store, you should already be able to preload the game in preparation for launch.