Table cache hit rate is 0% - is that a huge concern?
The query cache was only hit 400 out of 1,000,000 times.

That is a query cache hitrate of 0.04 %

This indicates that 99.96% of your queries are unique and are not reusable. That's not unusual if your are storing session data, doing blogging, audit trails, or just plain logging of events.

While you could setup slow query logging, there is a better approach to checking on SQL performance. I recommend using pt-query-digest with --processlist option or --tcpdump option

This will allow you to catch bad queries in the act of being bad.