1. Reliance on Google Docs' uptime. While any monitoring service will in theory present the same problem, you're putting all your eggs in one basket.
2. It's just the wrong tool for the job. Install and learn Nagios or Zabbix or what-have-you. If you're worried about uptime, get a couple VPSes from different providers and run your monitors from both.
There's nothing utterly horrifying about it technically, but I just can't imagine how one comes up with this answer to the question of monitoring services.
Ok, but as you pointed out, #1 is just as bad as using any other single provider (which isn't implied or suggested anywhere here). I disagree with #2. The results are pretty nice, and they're accessible through Google Docs, which is great for sharing with co-workers who aren't in IT.
For what it's worth, Google Docs isn't our only monitoring system. We use Munin as our primary monitoring tool, but this is a nice addition to that.
Funny you mention this because we use Nagios to monitor the availability of Google apps (Drive & Gmail mostly) and I get a false positive about once a fortnight. It's proven much more helpful to just monitor HN/Reddit or Twitter to figure out when there's an outage.
Do you make API calls, or just grab web pages? I've noticed the Google APIs seem to occasionally return errors for no apparent reason. You could try double-trying in your Nagios check.
It's also complicated by Google's infrastructure — services are scattered across many, many servers, and Google's outages tend to be on some subset of services and/or servers. Your Nagios checks are probably not always checking the same endpoint as users connecting.