Which is correct:
- Today is one of the warmer days this month.
- Today is one of the warmest days this month.
I hear the first used almost exclusively on television news.
Both are grammatical, but they mean different things.
The first supposes that several days this month have been warmer than the others, and that today is one of them. For example, the temperatures on 2, 8 and 19 September have been 16, 14 and 23 degrees and the temperature today is 18 degrees. All the other days in the month have been cooler.
The second supposes that several days this month have been the warmest this month, and that, again, today is one of them. For this to be true, the temperature today and several other days must all have been, for example, 20 degrees, when the temperature on all other days has been lower.
A superlative adjective is just that, and there can only be one warmest day. A day can be warmer than another, but in any given period, there is only one warmest day, just as there can be only one best, tallest, largest, busiest, etc. I think this is the most common error I hear--you notice I didn't say "This is one of the most common errors I hear," because that is not the proper use of the superlative vs comparative.