This is about subject-verb agreement: when the subject is singular, so should the main verb be; when the subject is plural, then the verb should be in plural form. (Of course, this only applies to languages where verbs are conjugated and not, for example, Standard Chinese.)
This rule is easy to follow when subject and verb aren't separated by many words, but authors may "forget" the subject's grammatical number if one of the many words between the subject and the verb has a different number. This can also occur if the subject is very complex ("the construction [of the sentence is] involved]", in Lovecraft's words). This type of separation of subject and verb is also known as a subject-verb split.
Below is a simple example from kgbanswers.com:
The teacher along with his students are going on a field trip.
The subject ("The teacher") is singular, so the main verb ("are going") should also be singular. However, due to the phrase "his students" (plural), the author got confused and put the verb in plural.
What Lovecraft is saying is that the risk for the above type of mistakes is higher, when sentences are longer (more specifically, when there are more words between the subject and the verb) or more complex ("involved").