Rav Falk is considered a godol by the other gedolim. Frankly, no one has ever cited here any, not a single one, specific Rov who disagrees with Rav Falk on even a single issue he discusses in his Sefer. I challanger anyone: name a specific rov who disagrees on a specific issue. Name the posek and the issue he disagrees with HaRav Falk shlita on. Although I’m sure there is some rov somewhere who disagrees with him on something somewhere, by and large everything he writes in his tznius sefer is agreed to by the poskim across the board. Hence the popularity of his sefer. (Otherwise everyone wouldn’t always be constantly discussing Rav Falk’s sefer over and over again. Check the old discussions.)
I’m waiting for specifics. I highly doubt they’ll be forthcoming, though I’m sure we’ll hear a litany of excuses why they don’t want to “mention” which rabbi.