Many languages, in order to distinguish between the past, present and future, have something called "tense". This trope happened when someone makes the other common mistake of amateur writing: unintentional tense shifts.
Just like how a lot of people were unable to ether spell or use words propitiatorily, so, too, do a lot of people have trouble maintaining tense. Usually, it involved shifting between past and present tense (there isn't a whole lot of future tense in fiction) and seems to most often come up in Dialogue.
For example, this sentence is written in present tense. If a less experienced writer inserts a quote in past tense here, like "He trashed the place!", they tended to fall into the past tense of the quote.
More often, the issue was that characters are speaking in the present tense while the story was being told in the past tense, and the writer has trouble switching from the immediacy of the dialog to the narration perspective, so you got things like this:
He looked up. "The sky is falling!" he says.
The correct tense usage would be:
He looked up. "The sky is falling!" he said.
He looks up. "The sky is falling!" he says.
People tended to relate experienced events in the past tense (as one would have expected) but relate events they are creating in the present tense (as they are creating them). This switch in tenses was used to judge the veracity of witness statements. It also explains why authors might drop into the present tense when they got to writing the bit of the story that they aren't planning out to begin with.
Oddly enough, the above description fit Japanese prose writing pretty well, as states of being are generally described in the present tense if they were in the "present" of the narrative. (Singular acts, such as dialogue, are generally reported in the past tense.) It also had no "tense agreement" rule for embedded sentences, so that dependent clauses need not take the same tense as that of the overall sentence: the sentence "She thought that he was in the kitchen" would have been more literally rendered as "She thought that he is in the kitchen". Of course, attempts to use the Japanese language in English-language Fanfic usually resulted in a completely different trope...
In English and many romance languages, an additional confounding factor is the notion of verbal mood, which unfortunately shared similar patterns of conjugation as verbal tense. Most writing in English is in the Declarative mood, and follows the normal rules for tense conjugation. However, if a person wished to convey possibility, desire, or something counter to fact, they might use the Subjunctive mood, which if used properly looked like hideously incorrect usage of the normal declarative mood. Constructions in the subjunctive mood sound like "if I were...then I'd be", and so forth.
Confusion also arose with the perfect tense, technically called an aspect. "He saw them in the kitchen" and "He has seen them in the kitchen" mean subtly different things. The past perfect served as a double past, but for constructions that ought logically to use a treble past, English grammar shrugged and breaks its own rules: 'She thinks he did it', and 'She thought he had done it' but 'She had thought he had done it'.
Another common tense issue is the progressive aspect. "Doing X, he did Y" meant that he did X and Y at the same time, not that he did X followed by Y. For the latter, you would say "Having done X, he did Y" if X and Y were related actions, or "He did X, then he did Y" if they aren't. This is described in the Turkey City Lexicon under "Not Simultaneous".
Related to this trope is Time Travel Tense Trouble, where a conflict in the chronological order of history versus the order in which the character(s) or audience experienced it created confusion.