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Whenever I write anything, I try to write it as correctly as possible without obsessing over it. For example, if I'm writing emails or blog posts, I would make the effort to make sure my spelling and punctuations are mostly correct by paying attention to them as I write. After that, I might do a spell check, but I wouldn't necessarily worry about every comma or semicolon. The key is to make sure that everything is readable, and correct for "normal" people, as opposed to Grammar Police.
For my journals, I take the same approach. I don't like reading things without any sort of punctuation or with excessive spelling errors, so I never write like that. I want my journals to reflect my language skills, not my laziness. But I'm little less strict with journals. If I am writing really fast because I want to get the words out then I don't worry about spelling or grammar. I do it as best as I can while maintaining the speed. And that's okay, because in those entries, it's the emotion that matters. Punctuation on the whole is there anyway (because people who write without commas and periods should be severely punished), and spelling errors are more due to speed. But on the whole, I would say that yes, grammar and punctuation does matter. I believe that if I am going to do something, I might as well do it well. That applies to journaling.
What do you think? Do you care about grammar and punctuation in your journal entries? How much do you care?