It really depends. Here are some things which *might* occur:
Lexicology: Perhaps some confusion over words, using more esoteric words instead of more casual ones. For instance, you might see someone saying "proposition" instead of idea (or something like that), because they believe it's more prestigious and they're trying to affirm that they're fluent in the language. Of course, this doesn't reflect their original language, but it reflects that they perceive a need to demonstrate that they are capable at English. These substitutions can also occur if individuals aren't fully aware of the nuances of words, and might reflect their original education in english.
Semantically: The most common example would be people translating directly from their native tongue. For instance, a french speaker might say "I have hunger" instead of "I'm hungry", because in french, the verb to have is used. There are probably many other examples.
Discourse: People might use certain titles (like Miss) even though it doesn't seem appropriate. The speech might be syllable timed (instead of stress timed), and they might use more or less hedging expressions.