This may seem like common sense, but it is worth mentioning: everything happens in context. When conducting an analysis, look at what is going on for different time periods. As said in an earlier post, you should also weigh it against industry benchmarks (This is also an option in many analytic tools under benchmarking in the visitors metric).
Keep up with current events in your office: consider the context of what your company is doing that might be impacting your website metrics. For example, is there a new direct mail campaign- that might explain the unseasonably high number of direct visitors in June.
Product lifecycle also has a place here. If you are working in an emerging market, then your website visitor numbers should be on the rise to keep pace with the growing market. If your product market is mature or in a stagnant state, don’t just sit there! Continue your efforts to expand market share for those visitors, and continue positioning the site to be ready for a market shift.