It really is worth double checking spellings and grammar are correct before sending anything out. You don’t want to give “silly” reasons for an agent/publisher to turn you down. The only reason should be your work is not right for them. Also there is a presumption if you can’t be bothered to check things like this the rest of your work will be littered with mistakes. Nobody has the time to correct these mistakes – it is what you as the author should do.
Other Writing Blogs
Read other writers’ blogs (look for those with a good record in the profession) as you learn a lot from these, including how to present a good blog! You learn a great deal by absorbing. Follow a few good blogs (if only to make sure you still have plenty of time for your own writing). If you decide to set up your own blog, plan it well before you start so you have plenty of material to “feed” it.
Subscriptions
Take out subscriptions to writing magazines. Have a go at the competitions. Enjoy the read. Take in how author interviews are done. Learn a lot! See these magazines as taking your interest in writing seriously. And they are great to relax with too. Build up short story successes (listings, winnings etc) to help build up a writing CV. There is some prestige from winning or being listed in these magazines.