Instant Replay Mode
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Information:

The infamous Instant Replay mode. For 12 years, it was unusable, and nobody knew what it actually was like. Now though, you can experience this awesome mode for yourself.

As awesome as this is, keep in mind that Angel Studios cut this mode for a reason. I've thoroughly tested this mode out, and have come up with a list of roughly what works properly, and what doesn't. 
First of all, any races that involve opponents, even just 1, will always fail. No exceptions. I've tested this many times, and haven't had a single accurate replay. In each of them, my car runs off the course and usually slams into walls for the remainder of the race.
This also seems to happen any time you have your time of day set to Night. In every single night run I've tested, my car does something totally different than what I really did.
Also I feel like mentioning that I had one failed run in Evening. I tried to reproduce the failiure afterwards to confirm, but it didn't fail on me again. I've tried various runs in Evening since, and all turn out fine.

Also, replays have a maximum length of 5 minutes, and it captures the FIRST 5 minutes of it. After this limit, the replay simply cuts off. Currently there is no way to bypass this limit, although it makes sense. Computers back in the day didn't have much RAM.

Besides these issues, it seems to work fine. Traffic density, Pedestrian density, and Cop density don't seem to have any negative effects. I've played various (and even recorded a couple!) replays that take place in a Noon Cruise, with no issues. However, just because it works fine for me in these situations, don't expect perfection. Again, Angel Studios cut this mode for a reason. Regardless though, enjoy this awesome hidden mode!
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Bugs:

As of right now, you can't actually save replays. To use the mode, click the new Instant Replay button on the main menu, and click Load. You can then drive around with keyboard controls, hit Rewind, and Play to view what you just did. You can adjust settings in the race menu.
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Installation Instructions:

Copy the EXE, the AR and the RPL files into your Midtown Madness 2 directory, located at:

Windows Vista/7 - C:\Program Files (x86)\Microsoft Games\Midtown Madness 2
Windows XP - C:\Program Files\Microsoft Games\Midtown Madness 2

The EXE is a using the XP Patch, Speedboot and No-CD. So it should work for anyone.
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Credits:

Aaro4130 - Spending alot of time getting this mode to work. This would simply not be possible without him!
_DB_™ - Fixing up the menus to make them look better. I also wrote this readme and did extensive testing.