I just received a:

Model Name: PowerBook G4 15"
Model Identifier: PowerBook5,8
Processor Name: PowerPC G4 (1.5)
Processor Speed: 1.67 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 2 GB
Bus Speed: 167 MHz
Boot ROM Version: 4.9.5f3

That I want to use as my second, and portable, MorphOS computer. Before I install and purchase the license, are there any potential issues or things that I have to consider or keep in mind while using this laptop as a MorphOS dedicated computer?

Besides that it is the best G4 MOS computer that you can get - no

Actually, it can be that your CD-ROM drive fails now or after some time. Also the battery is weak in most Powerbooks. But both can be replaced. So if this runs fine then you can enjoy MOS on it.

The fans also seem to be a weakpoint. I have bought a replacement PB (same model as yours) and will swap my right fan, which got pretty noisy.
If you have basic knowledge of fixing and assembling computers this should be no problem.

Also, the USB:s are very weak.

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For instance,even though I haven't yet installed MorphOS in this laptop, I was trying to connect an external HDD using a USB connection, and the laptop couldn't read it. I'm guessing it'd need drivers, since this external HDD is a lot more modern and maybe incompatible.

Other USB devices I tried worked fine, USB memory sticks, multi card readers, etc.

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You did't need a driver, but a external power source for the hdd. Use a active hub, and the hdd works.

Yes, the USB:s are too weak to drive an HDD without external power.