There's a civic election brewing in my part of the world and thus a
new mayor will be elected. There's been a lot of coverage on this subject on a local radio station, of course, and I was shocked to hear a seasoned newscaster (who ought to know better) pronounce the word "mayoralty" with the accent on the syllable YOR. I've always
been told that this word was pronounced exactly like the word "mayor" is normally pronounced with the "alty" added to the end. Am I wrong here?

Merriam Webster agrees with you, 'mA-&-r&l-tE or 'me-&-r&l-tE; even showing a third pronunciation with the -yo-completely missing 'mer-&l-tE. I would suspect influence of words like minority or majority with emphasis on the second syllable.