The Shela in the beginning of Mesechtas Yoma - paragraph beginning with וכך הוא המנהג mentions saying דיינים מומחים in the context of saying it in front of a group of Talmidei Chochomim (wise scholars) and Yirei Shomayim (God-fearing people).
Orchos Rabeinu 2 page 171 mentions that the Steipler omitted the word "מומחים."
However, Rabbi Shlomo Kluger Zatzal, in the newly printed Nidrei Zerizin Volume 3 - 228:14, says that it is being done as a matter of respect. He claims that it is not considered falsehood, because people do this type of thing often. He proves this from Shulchan Aruch Even Hoezer 129:7, which says that adding inaccurate honorific terms doesn't invalidate divorce documents once it's done. Therefore, we shouldn't change the accepted nusach (formula). (I would add that in today's age many people are called R', Reb, or Rabbi even though they are not.)
Halichos Shlomo 2, in the introduction to Shalmei Neder, says that Rabbi Shlomo Zalman Auerbach Zatzal used to say "דיינים מומחים" as it is printed in the Siddurim.