However, I was referring to the actual usage of the definite article, not its spelling. I think the problems here are of two different kinds:

Those who come from languages where there is no definite article (e.g. Chinese, Turkish) struggle to understand the correct usage. This is one of the most common glitches I hear from my Mandarin speaking colleagues (in addition to omitting plural forms).

Not all IE languages have articles, i.e. Hindi, Russian, Latin. Simplifying thing, one may say that English is a curious mixture (or bastard :-) of French and Anglo-Saxon, both of which has articles. It shed a lot of its grammatical rules over the centuries (e.g. noun declension, verb endings) but still carry vestiges, like the appendix, which is what confuses other IE speakers. These errors, tend to be the opposite of the Mandarin case, i.e. the over-regularization of the usage. My wife, who is near-native in French, does this frequently in her English usage.

This brings to mind a slightly different topic: The prediction of gender for (genderless) words adopted from English, i.e. if you are German and see the word iPad for the first time, which gender do you use? This study (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.132...) tackled this problem for Scandinavian languages and found that it is quite difficult, they get ~70 accuracy.

The working class accent for where I'm from (Dublin, Ireland), prounounces "th" as "d", so "the" can be said "de".

A german friend advised his mother (who's is an english teacher (in germany)) to teach her students this, since it's easier for germans to pronounce!