From reading Wikipedia, it sounds like historians generally accept that the pontoon bridges did actually happen. But there appear to be a lot of specifics that are disputed, and it can be reasoned that many points of Herodotus' descriptions would be problematic from a technical standpoint.
Has any physical evidence of the bridges ever been found? Has there ever been an attempt made to find any? Divers or underwater craft looking for evidence?
After the crossing, the bridges were left behind. When a part of the Persian army later retreated to the Hellespont, they only found the debris of the bridges destroyed by another storm.[9]
Could we expect to find any anchors, or fragments of sunken boats, or anything of the like down there? I have no idea if it's even feasible to expect such things to last 2500 years, or to remain stationary.
No. To my knowledge no physical evidence of the pontoon bridges has ever been found and I would not expect any to be found today. There are several factors that would rather quickly destroy any evidence of them in the Dardanelles. First of all the Dardanelles are comparatively shallow. The Black Sea is notorious for preserving wooden ships almost indefinitely but that is due to its depth and hypoxic conditions there. The Dardanelles are much more shallow and the current there is strong, the bottom does not have the hypoxic conditions required. Simply put, any organic evidence would long since have been destroyed.
As for other things like anchors, well, it's one of the most heavily trafficed sea lanes in the world and has been so for 3000 years. Even if you were to find an anchor or some other inorganic part, how would you know it was from Xerxes' crossing?