Do not install play disc for the 360 version.  No reasons why yet.

@TurianKnight We do not recommend that.

— Rockstar Support (@RockstarSupport) September 15, 2013

EDIT:

Eurogamer explains why:

http://www.eurogamer.net/articles/2013-09-16-rockstar-warns-dont-install-gta5-xbox-360-play-disc

"Rockstar recommends that you shouldn't install the GTA5 play disc on Xbox 360 and it's sound advice," Digital Foundry chief Richard Leadbetter said.

"When you first get the game, the first order of business is installing the mandatory content from disc one - this accounts for 7.7GB of data to install on your hard drive. Now, there's absolutely nothing stopping you installing disc two - the 'play' disc - onto the hard drive too, using the Xbox 360's dashboard to do so. It takes up an additional 7.8GB of storage. However, doing so impacts the game's ability to stream texture data, resulting in regular pop-in of in-game objects and textures.

"So what's the story here? Well, optimal streaming is achieved by making us of all the available bandwidth in the system. Why stream just from the hard drive when you can run in data simultaneously from both the disc and the HDD? Based on what we're seeing on the Xbox 360 version, perhaps running both DVD and HDD assets from just the one source slows down access times, impacting streaming performance. It's not game-breaking stuff, but it does take you out of the moment when it does manifest and for that reason we can't recommend installing the play disc.

"GTA5 isn't available for digital delivery on Xbox Live, but we are curious what the impact - if any - will be on the PS3 version, as that is available as a PSN download. The Digital Foundry Face-Off - due tomorrow morning at 11am - is based on comparison of the two retail disc versions of the game."

ORIGINAL STORY: Rockstar has warned Xbox 360 gamers not to install the Grand Theft Auto 5 "play" disc.

On Xbox 360 the openworld game comes on two discs: one mandatory "install" disc and one "play" disc, both around 8GB in size. It's a similar situation to Forza 4, which also shipped on two discs on Xbox 360.

Prospective GTA5 owners - some of which already have the game as a result of early shipping from Amazon.co.uk - might have wanted to install both discs, but Rockstar recommends against it.

"For optimal performance, we recommend not installing that disc," tweeted Rockstar Support.

Then, "An 8GB install is required. For optimal performance, we recommend not installing the play disc."

Rockstar has promised more information soon. For now, the upshot is, with GTA5 on Xbox 360, you have to install disc one but run disc two from the drive.

You probably install disc one and just play off disc two. No disc swapping needed. Halo 4 does it, just the disc numbers are opposite.

Strange, all it normally does is reduce load times and helps your disk play smoothly if it has scratches.

That would be ideal, but why not install both and play off one?

I can't think of a single reason for this. I don't like it, though. I'm sure it wouldn't happen often but I remember how pissed I was when I played Metal Gear Solid 4 and I was ready for the game to continue. Instead, I had to wait for the game to install. I think I'll get flashbacks with GTAV.

maybe its been glitching the game and until they can patch it they recommend that you dont. games always have day 1 issues these days that get patched fairly quickly

I would imagine that is the case, of course people should not have the game already... they should have to wait like the rest of us

No problem with me. It is install, right? No internet requirements?

The reason will be the game will do simultaneous reads from HDD and DVD Drive, putting both disks on to HDD, will just increase load times, this has been seen before in Halo Games.
Installing is not always the best option on 360.

I think I got the gist of it.  Metal Gear was on one disc and had to install between chapters.  From what I can tell (I prefer to install discs like I did with Mass Effect 2 and 3), somewhere along the way, I'll finish disc one and have to install disc two.  Right?

*edit* and if I had to go back to disc one (for example, if somebody else wanted to play and we were on different discs), I'd have to uninstall disc 2 to reinstall disc one.  If that's not what this is, I apologize for jumping to conclusions.