Well, it is in the US anyway. There are many people who are against the idea of a grammar day - people who are pro-grammar tend to be annoying and of the prescriptive persuasion rather than descriptive. More details here.
Still, I think anything that gets people thinking about language is, in my humble opinion, not a bad thing.
Here's a handy list of tips to improve your writing/grammar :-)
BTW - here are some other language-related days
National Handwriting Day - January 23 (missed this one)
International Mother Language Day - February 21 (missed this one too!)
National Punctuation Day - September 24
English Language Day - October 13
Dictionary Day - October 16