Is my MacBook outdated?

I own a white, first generation Macbook. The specs are: 3.3" Notebook PC (1.83 GHz Intel Core Duo, 512 MB RAM, 60 GB Hard Drive, DVD-ROM/CD-RW Combo Drive). I can't do most basic productivity (like Microsoft Office) and games (among other software) due to a "shared library error". The case has a defect which causes it to have sweat stains. Besides that, the computer is fine, still pretty fast. Even though the computer is a little bit over 1 year old, should I pick up a new one?

There's no reason why you shouldn't be able to run MS Office for Mac. You should reinstall the OS then install Office for Mac.

As for your computer being outdated, if it's doing what you want it to do then your computer is fine.

Shared library error is a Microsoft Office software problem, your MacBook is fine. You can try and reinstall the software. The only thing I would do is buy another chip of RAM and kick it up to at least 1 gb. The sweat stains defect Apple will repair, replace for free under warranty. Call Apple and find out what they will do for you.