I had experienced a couple lockups while playing. Nothing very frequent, but irritating. Left me worrying if my brand new console was going fail me and need an x-clamp replacement, heatgunning, etc. No warranty for me, as I had opened the thing within a week of getting it.
So one day I took it over to a friend's house to play, and after playing for quite a while, one game was taking longer than usual to load between areas. Then it froze, but the console came back to life after I ejected the disc. Hmm... I always play games installed to the HD, so I uninstalled the game and played it from the disc. It was fine.
After playing fallout for another long time (from HD) it decided to freeze on me, which was alright since I needed to leave anyway. The next time I connected it back at my house, it didn't load my profile on startup. The console wasn't recognizing my HD at all. I shut the thing off, looked at the drive, it was seated in there just fine. So I pushed on it a little, and then turned on the console. It came up and worked.
This made me happy, as it meant my console wasn't dying after all, but it did mean that I needed to do something about this HD. I could get another enclosure, try my luck, or I could do the internal mod.
BTW, I haven't had any problems since doing it.
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So here's my take:

This is the placement of the drive. I used servo tape on the underside, and it mounts very securely.

The SATA cable I used actually locks onto the drive, less chance of it slipping out I guess.

I heat shrinked the clipped leads just for safety.

All the ground connections on the hard drive from both the SATA and power cables were all directly connected. I decided to clip off the ones in the SATA cable. This allowed me to pass the data wires through pre-existing holes, with having to route a bare ground wire or cover it.

The wires line up perfectly, as per Plasmastorm's post above.

I routed the power and ground wires the same way as the data, through a couple larger holes. I used the same color for both, only because that's what I had on hand that size. I paid attention to not mix them up. I decided to use the 5v supply that was going to the drive originally, instead of some other board location. This is just because I know for sure that it's not going to cause any problems from drawing power there.
I originally intended to use the center pin (not the same row as the SATA connections!) for the power, but the wire wanted to lean towards the other. That's fine, they're both tied directly together. There was one more 5v, I think on the other side of the one I used, but I'm not certain. You can always check what has 0 ohms with that center pin.
Several of those pins were ground, again, check with multimeter. I decided to use the big one for obvous reasons.

I cut a hole in the heat shield (and trimmed down plastic). Another thread had mentioned about it pressing down on the drive causing problems. It did press on the drive, so I made room.
Also, I should note that I reinforced a few areas (like where the SATA wires passed through the board) with hot glue.