Chad Gadya (recited at the end of the Passover seder) is written in a mix of Hebrew and Aramaic. Specifically, most of the verbs are in Hebrew, except for זבין (bought) and אתא (came), and most of the nouns are in Aramaic, except for HaKadosh Baruch Hu, Malach HaMaves (angel of death), and HaShochet (slaughterer). Why?
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The first attestation of Chad Gadya in print is in the Prague Haggadah of 1590 (online source). It is thought by some to have been modelled on a German folk song, and thus composed at such a time as Aramaic was no longer being spoken. This may account for what some have seen as grammatical errors within the text (online source).
An example of a "grammatical error" (taken from that website, which is in Hebrew) is שונרא... דאכלה ("the cat... which ate"). Aside from possible problems with vocalisation, which may be found in other passages in Chad Gadya also, שונרא (cat) is a masculine noun, but אכלה (ate) is a feminine verb. Really, the text should say either שונרתא (which is the feminine word for "cat") or דאכל (which is the masculine verb, "ate").
In any case, an admixture of Hebrew and Aramaic in mediaeval Jewish literature (a time when people are neither speaking Aramaic nor Hebrew outside of liturgical settings) is par for the course, and is the result of both languages being read with roughly equal frequency. Hebrew, the language of scripture and prayer; Aramaic, the language of scholarship.