Spontaneous real-life speech is imperfect in many ways. It contains disfluencies and ill-formed utterances and has a highly variable rate. When listening to spontaneous speech, the brain needs to contend with these features in order to extract the speaker’s meaning. Here, we studied how the neural response is affected by four specific factors that are prevalent in spontaneous colloquial speech: (1) the presence of fillers, (2) the need to detect syntactic boundaries in disfluent speech, and (3) variability in speech rate. Neural activity was recorded (using electroencephalography) from individuals as they listened to an unscripted, spontaneous narrative, which was analyzed in a time-resolved fashion to identify fillers and detect syntactic boundaries. When considering these factors in a speech-tracking analysis, which estimates a temporal response function (TRF) to describe the relationship between the stimulus and the neural response it generates, we found that the TRF was affected by all of them. This response was observed for lexical words but not for fillers, and it had an earlier onset for opening words vs. closing words of a clause and for clauses with slower speech rates. These findings broaden ongoing efforts to understand neural processing of speech under increasingly realistic conditions. They highlight the importance of considering the imperfect nature of real-life spoken language, linking past research on linguistically well-formed and meticulously controlled speech to the type of speech that the brain actually deals with on a daily basis.