There are several different festival calendars in the Pentateuch, and each one originally belonged to a different textual tradition: Ex 23:14-19 (E); Ex 34:18-23 (J); Deut 16:1-17 (D); and Lev 23 and Num 28-29 (P). When compared against each other, one notices minor differences in festival names, their dates of celebration, and even the place where they were to be celebrated. We will look at these contradictions at a later date.
Presently, we are only interested in the discrepancy between the date of the festival of Unleavened Bread in the Priestly version of Exodus 12:14-20 and, surprise, surprise, the Priestly version found in Leviticus 23 and Numbers 28. So even within this corpus of literature that scholars identify as the Priestly source, there were discrepancies. In fact, Leviticus 17-26 has long been identified as a separate redactional layer in the Priestly source which is intensely interested in holiness and ethical/ritual purity, and has thus been dubbed by scholars as the Holiness Code.
In this particular case, both Leviticus 23:6 and Numbers 28:17, which are practically duplicate versions, state that the festival of Unleavened Bread starts on the 15th and not the 14th as stressed in Exodus 12:18. This contradiction might be more apparent than real, since academics have postulated that the discrepancy might be reflective of the difference between using a solar and lunar calendar system. Such debates emerged in later Judaism.