Archaism is an obsolete form of speech or writing.

Pleonasm (from Greek, pleon: more, too much) is the use of more words or word-parts than is necessary for clear expression: examples are black darkness, or burning fire.

Some grammar experts claim that the fewer prepositions the better, and this check warns you if the ratio of prepositions is more than 1 preposition per 5 words.
Abundant prepositions: The data from the participants of younger age in this study were compared with those of subjects of older age by an analysis of variance.

A phrase like “a good congressman knows his duty” excludes women, and it may show good style to rewrite such a sentence in a gender neutral form, like "good representatives know their duty". Check the references for more info on techniques to avoid gender bias in your wriitng.

Avoid using long strings of modifiers or nouns. These stacked modifiers and nouns can be hard to read and sometimes create ambiguity. Add a few words (especially prepositions and conjunctions) to make the relationships between nouns clear to the reader.

Weak Example

Previous work has shown that a purified pro-oxidant, vitamin E-deficient fish oil diet protects mice against malaria parasites.

Improved Example

A split infinitive is an English-language grammatical construction in which a word or phrase, usually an adverb or adverbial phrase, comes between the marker to and the bare infinitive (uninflected) form of a verb. Many scholars consider it as bad style.

While an adverb ending with -ly has no grammatical problem, many consider it as bad style. Straight from "On Writing Well, 5th Edition" by William Zinsser: "Most adverbs are unnecessary. You will clutter your sentence and annoy the reader if you choose a verb that has a specific meaning and then add an adverb that carries the same meaning. Don't tell us that the radio blared loudly - "blare" connotes loudness. Don't write that someone clenched his teeth tightly - there's no other way to clench teeth. Again and again in careless writing, strong verbs are weakened by redundant adverbs."

Expletive constructions begin with "there is / are" or "it is", and their variations. These do not add any meaning, and can be easily replaced for example: There are twenty-five students who have already expressed a desire... can be easily rewritten to Twenty-five students already expressed a desire...