/T͟Hē/ is pronounced before words that start with a vowel and /T͟Hə/ before consonants, but I noticed that most of the time I pronounce 'the' /THe/ as in 'there', with a short e for both cases. Does it really matter? How severe is this mistake?
I pronounce 'the' as in 'there'
The pronouncation of 'e' in 'there' is similar to 'air'.
air: /ˈɛəɹ/, /ˈɛɹ/
Does it really matter? How severe is this mistake?
From the description so far, it sounds like you would be easily understandable. It wouldn't block communication. At the same time, you will sound like you have an accent. This isn't necessarily a bad thing. Often accents are charming and pleasant. Also, it helps to signal that the other person should perhaps speak a little slower, or not take for granted that you are completely fluent. If it reaches a point where you do want to communicate the message "Actually, I am absolutely fluent, practically a native speaker", then you may be more impelled at that time to modify the 'e' sound.