Erratic doesn't have a meaning related to error. It means eccentric, or unsteady instead. Error has its adjective form as erroneous and errant. So what is the noun of erratic?
ODO shows erraticism as the noun.
not even or regular in pattern or movement; unpredictable:
It is related to error in that they both stem from Latin errare, to stray (from the truth in one case, from the straight and narrow in the other).
Though the erraticism of India’s monsoons is fairly documented, research provides ample proof that global warming has added to the unpredictability and erraticism of the same.
Erratic is also a noun.
an erratic or eccentric person.
Geology . an erratic boulder or the like.
OED returns several example sentences with erratic and erratics as noun forms.
Eg. Bacchic priests.... erratics or wanderers
Erratic is derived from a Latin participle of erro, the verb for "to wander, to stray" from which error is also derived. One might gloss it as "tending to stray from a regular course." Even error has this original sense of being "off-course."
As a comparison, the word "eccentric" literally means "off-center," and so metaphorically "wandering from a circular or regular course." There are two obvious noun forms. An "eccentric" is someone or something that is eccentric. Eccentricity is the tendency to be eccentric.
Nouns derived from erratic, however, tend to be non-standard: you are unlikely to hear anyone speak of "erraticness," "an erratic" (as in a person, though there are specialized vocabularies where this form might be used), or "erraticism." One is far more likely to use "irregularity" or "instability" or some other word.
erraticity: Event-to-event fluctuation
To quantify the chaotic nature of the event structure, a new measure called the erraticity was introduced.
A definition: (! .pdf)
erraticity (ĭr·ə·tĭs’·ĭ·tē) n. The quality or state of being erratic, characterized by the lack of consistency, regularity or uniformity.
Usage Example Phys. Rev. C 68
Event-to-event fluctuation in multipion production in 32S-AgBr interactions at 200AGeV has been investigated in terms of the newly defined erraticity measures χ(p,q), χq′, ωq, μq′, and rq proposed by Cao and Hwa. A comparative analysis of experimental data with that of random data and VENUS data reveals erratic behavior of the multiplicity moments signifying chaotic multiparticle production in ultrarelativistic nuclear interactions. (Erraticity analysis of multipion data in 32S-AgBr interactions at 200AGeV)
There are several instances of the term's use in research papers.
Not to be confused with the words of the same spelling, erraticity (paranormal studies): 'the state of errant spirits, that is, disembodied spirits, during the interval between two material existences' or, erraticity (nonce): 'a state of being so uberly erratic...emotionally, physically, and mentally.' :)