It brought back results from other months that occured on the same day.

I posted wrong request :( But it can be easily extended to become right:

-- today
SELECT * from `your_table_name` WHERE 
  YEAR(time) = YEAR(NOW()),
  DAYOFYEAR(time) = DAYOFYEAR(NOW())

--this month
SELECT * from `your_table_name` WHERE 
  YEAR(time) = YEAR(NOW()),
  MONTH(time) = MONTH(NOW())

--this week (USA) (simple solution with WEEK() 
--won't work at the beginning of the year
SELECT * from `your_table_name` WHERE 
  YEARWEEK(time, 0) = YEARWEEK(NOW(), 0)
[download]

Rewriting of the request to use DATE_FORMAT can be performed according to the docs.

I don't know if it's a Perlish way, but it's a RIGHT way. SELECT must select only the data you want, and it's faster and cleaner to perform all heavy-weight data filtering on the database side.