Can't come up with anything on the spot. But sometimes I see text I wrote and think why I put "a" or "the" instead of vice versa. Sometimes it's just not clear enough wether this item is specific enough or not.
On the other hand, I omit article completely more frequently than using a wrong one. I find I have to consciously think if I should use an article and which article should I use. When I write/talk quickly without double checking, shit happens. Even after using English a lot for 2 decades, articles is just a foreign feature that I have to use consciously.
A == non-specific The == specific
'A dog' could be any old dog.
'The dog' is a specific dog we know.
Thus
A == any The == thing
Perhaps I'm not clear where with this understanding it would trip you up. Can you think of an example?