Some examples of reversible error would be erroneously instructing the jury on the law applicable to the case, permitting seriously improper argument by an attorney, admitting or excluding evidence improperly, acting outside the court's jurisdiction, injecting bias into the proceeding or appearing to do so, juror misconduct, etc.
sˌʌm ɛɡzˈæmpəlz ʌv ɹᵻvˈɜːsᵻbəl ˈɛɹɚ wʊd biː ɛɹˈoʊniəsli ɪnstɹˈʌktɪŋ ðə dʒˈʊɹɹi ɔnðə lˈɔː ɐplˈɪkəbəl tə ðə kˈeɪs, pɚmˈɪɾɪŋ sˈɪɹiəsli ɪmpɹˈɑːpɚɹ ˈɑːɹɡjuːmənt baɪ ɐn ɐtˈɜːni, ɐdmˈɪɾɪŋ ɔːɹ ɛksklˈuːdɪŋ ˈɛvɪdəns ɪmpɹˈɑːpɚli, ˈæktɪŋ aʊtsˈaɪd ðə kˈoːɹts dʒˌʊɹɹɪsdˈɪkʃən, ɪndʒˈɛktɪŋ bˈaɪəs ˌɪntʊ ðə pɹəsˈiːdɪŋ ɔːɹ ɐpˈɪɹɪŋ tə dˈuː soʊ, dʒjˈʊɹɹɚ mɪskˈɑːndʌkt, ɛtsˈɛtɹə.