For those who celebrate Yom Yerushalem,is Tachanun said during Mincha the afternoon before Yom Yerushalem?
The days that we do say tachanun at Mincha, even though we don't say tachanun the next morning are Erev Rosh Hashanah, and Erev Yom Kippur, and there's a dispute (in both the Ashkenazi and Sephardi spheres) about Pesach Sheni. Neither of these are "real holidays" in the same sense that Purim and Chanukah are.
Since I would think that Yom Yerushalyim and Yom HaAtzmaut are supposed to be similar to Chanukah and Purim, it seems to be reasonable that if you omit tachanun on Yom Yerushalyim or Yom HaAtzmaut, then you should omit tachanun at Mincha the day before also.
(No sources, just my sevara here. Consult your rabbi for a precise ruling.)
You do not say Tachanun at Mincha the day prior to a day that you do not say Tachanun other than if there is a specific reason to - see links above
If you do not say Tachnun on Yom Yerushalayim as some people do then you would not say it at Mincha the day before either.
Explicit instructions are given in the Rinat Yisrael siddur, widely used in Israel:
במנחה שלפניו אין אומרים תחנון, ואם חל בשבת אין אומרים צדקתך.
At mincha before it tachanun is not said, and if it is Shabbat, tzidkatcha is not said. (translation mine)
You can view this on Hebrewbooks.