What's a term or word to describe impassioned arguments or feelings about inconsequential things?

Solution 1:

Such a situation might, among many other things, be described as a melodrama, a storm in a teacup, or much ado about nothing.

Solution 2:

Petty means wasting time on the trivial. The matter itself is trivial, and arguing over trivial matters is petty.

American Heritage® Dictionary (Fifth Edition):

Showing an excessive concern with unimportant matters or minor details, especially in a narrow-minded way: petty partisanship

Picky is casual, only slightly less harsh. See pedantic for a fancier word, also no compliment.

For a euphemism for all these synonyms, use exacting -- If I think you are petty, you will think you are being exacting, at most.

2http://www.thefreedictionary.com/pedantic

Solution 3:

a mere trifle TFD

from trifle:

1. Of little worth or importance. 2. Frivolous or foolish:
2. a tiny bit; a small, unimportant matter;

Solution 4:

make a mountain out of a molehill

over-reactive, histrionic behaviour where a person makes too much of a minor issue

https://en.wikipedia.org/wiki/Make_a_mountain_out_of_a_molehill

Solution 5:

In some cases, it might just be healthy verbal sparring, which is comparable to being assertive. (This video actually teaches children how to properly engage in arguments with bullies, as a means to defend themselves from verbal or emotional abuse.)

And in other cases, it might amount to contentious, mindless bickering (meaning quarreling or petulantly contending with words).

Occasionally, it is the work of a scold, which traditionally was illegal if women did it.

It all depends on the attitudes involved, although it is nearly always obnoxious, loud, and annoying.