Detail #8: A gender-like thing but with verbs instead

A language where there are three or so classes of verbs. These classes differ in

• what affixes they take to mark different things
• what they mark (e.g. class I marks tense-aspect but no mood, class II marks tense, aspect and mood, but has a less fine-grained tense-aspect system, and class III marks tense, and every verb in it has inherent aspect that cannot be changed morphologically)
• details in the congruence system (class I has gender, person, number agreement for the subject; class II has no agreement, class III has person, number and gender agreement for subject, as well as a really minimal object-related agreement detail, as well as volition marking by means of reduced agreement)

They do not differ by 

• meaning - there's no set of meanings that unite all verbs in one of the class or exclude verbs from some class; auxiliaries can be found in all three. With these exceptions: all verbs of movement are class I verbs, all verbs of possession, exchange of possession and agreements and contracts are in class III.
• intensity, whether they are kinetic or not, transitivity, number of arguments in general, etc.

However, the classes also differ in some other ways:

• subject and object case; class II is somewhat ergative in behavior. Coordinations using nominative and/or accusative is permissible, though, for all classes.
• certain derivative affixes assign a derived verb to a specific class
• infinitives are marked for case according to what the auxiliary's class calls for

Several verbs can be finite in a clause, and which subjects and objects belong to which verb can be distinguished by case (as well as proximity to verbs, if ambiguity has to be counteracted by phrasing). The case distinctions are fewer in the plural than the singular, so this works best with singular subjects.

Detail #1: a possessive and a causative structure

In some language,
"nom₁ has an adjective nom₂" turns out

[nom₁] [verbalized adjective] [nom_2, oblique object]

whereas "nom₁ makes nom₂ adjective" turns out as

[nom₁] [verbalized adjective] [nom_2, direct object]

The marking as direct object or oblique object may be obtained by some kind of adposition if the language is primarily isolating (in which case I'd suggest the oblique object be the only one marked at all), and in a more inflecting or agglutinating language, an accusative or somesuch would probably fit the bill fairly well.

Short sketch #3: Dummy objects

Imagine a language where verbs are made more 'intensive' by adding an object of some kind.

Giving glosses, where "dummy" stands for "some dummy of some kind"

hear.2pl   = we (do) hear 
hear.2pl   it.acc = we listen 
hear.2pl   dummy.acc = (this) noise is annoying us

However, when introducing a real semantic object, this language does not permit the dummy to be the same case as the real object, and demotes it to some other case:

*hear.2pl throbbing gristle.acc dummy*.acc   ----> hear.2pl throbbing gristle.acc dummy.dat 

The same process repeats when an indirect object is added, etc. Different dummy cases have different hierarchies and will be demoted along different paths.

Sometimes, a dummy is repeated in different spots to increase the intensity:

rain.3.sg.  =  it rains
rain.3.sg it.acc = lit. "it rains it", ~it rains intensely
rain.3.sg it.acc it.instr = lit "it rains it with it", ~it's pouring down
rain.3.sg it.acc it.instr it.comitative = it rains it with it and it too, ~this rivals the deluge.
it.nom rain.3.sg. it.acc = the subject dummy probably works to make the rain somewhat more specific, such as "right now, right here, it rains intensely". In combination with a previously established location or timeframe or both being somewhat topical, it would be more likely to pertain to that location or time or both.

As for describing persons, adding such objects could be used both for positive or negative effects:
play (pertaining to instrument).3sg dummy.acc = he/she plays (his/her instrument) intensely well.
 give.3.sg dummy1.dat = put out
give.3sg dummy2.dat = he/she is slutty; the verb is only interpreted as referring to sex when with a dummy dative.

These dummies originate as nouns, often specifically differently strong profanities. This idea occured to me after I heard my brother use "satan" - a common Swedish curse word - as an intensifying particle after 'basa' (to emit bass tones), as in "an basar satan" to describe the volume of the bass sound emitting from an amplifier and its speakers.