Does one have to repeat the prayer if the worshiper made a mistake in saying "wa rahmatullah" (and the mercy of Allah) in the final taslim, while having pronounced the sufficient part of the salam, which is "Assalamu Alaikum" (Peace be upon you)?

It is sufficient in the wording of the taslim to say: "Assalamu alaykum" (Peace be upon you). This is the view of the majority of scholars, and it is sufficient. Adding "wa rahmatullah" (and the mercy of Allah) is a recommended addition. If the worshipper makes a mistake in the addition or omits it, their prayer is still valid.