Am I correct in assuming there won't be any issues installing SQL Server 2000 32-bit on a Windows Server 2008 x64 system?
I understand the memory limitations, etc, but that doesn't matter at this point.
SQL Server 2000 is incompatible with Windows Server 2008; that being said I have only ever tried to install it on Windows 7 (which shares the same code base as Windows Server 2008) and it outright rejected the install.
You might be able to install it but it will depend on the exact features that you select. For example: I know that you cannot install Reporting Services for instance because it depends on IIS6 which is not available for Windows Server 2008. There is a short section on SQL Server Central where someone has tried to install SQL 2000 on Windows Server 2008 and has come across problems.
If you must use SQL Server 2000 I would recommend putting it on a VM running a known compatible version of Windows Server - though to be frank, I'd rather move the databases to a higher version of SQL and run them in compatibility mode (though this may not be an option for you.)
I hope this helps you.
I'm not sure why you're installing SQL Server 2000 anywhere in the year 2012, but no, there shouldn't be any technical issue other than the ones you've identified and the fact that it is nowhere near supported.
In any case, there is no 64-bit version of SQL Server 2000 - there is only 32-bit for x86 and 64-bit for IA. I assume your Windows Server 2008 box isn't Itanium.
SQL Server 2000 is not supported on Windows Server 2008. If you simply must run it, I suggest building a VM with Windows Server 2003 and installing SQL 2000 on that instead.
If you mess up your Windows Server 2008, don't go crying to Microsoft. They will not be able to help you.
From an article detailing end of support dates:
If you are running Windows Server 2000 SP4, you should make plans now to upgrade to Windows Server 2003, Windows Server 2008, or Windows Server 2008 R2 (July 13, 2010 is the cutoff). Your Windows upgrade choice may also require the need to upgrade SQL Server.
Install MS SQL server 2000 via setup instead of AutoRun. Setup can bypass the compatibility check very easily.