Bad things:
- no security on user level: it's not possible to run a web server at non-root security settings (so even when compromised, it couldn't do much harm)
- no memory protection: there's no limit to what any compromised binary could do to the running system
- little attention from security experts, security flaws may go unnoticed for a long time
Good things:
- very exotic platform, so very little probability that a untargeted attack would find the right platform
- little probability security issues would even be explored by the experts
As long as you can't close the whole system for security (e.g. static content from a CDROM), I wouldn't run a server off of an Amiga.