iterator - no matching erase function in c++11

Question 1

You have three bugs here.

for (vector<File>::const_iterator it = this->files.begin(); it != this->files.end(); ++it) {
    if (...) erase(it); // break after, no need of ++it in else branch
}

The first bug is that you incorrectly cut-and-pasted your code into StackOverflow. What you meant to paste was

for (vector<File>::const_iterator it = this->files.begin(); it != this->files.end(); ++it) {
    if (...) this->files.erase(it); // break after, no need of ++it in else branch
}

The second bug is what the compiler is warning you about: there's no way to modify a collection through a const_iterator. (EDIT: Okay, apparently C++11 added such a way, but libstdc++ didn't support it immediately.) That's what the const_ part means! If you want to modify the collection, use a plain old iterator:

for (vector<File>::iterator it = this->files.begin(); it != this->files.end(); ++it) {
    if (...) this->files.erase(it); // LOOK OUT, THERE'S STILL A BUG
}

The third bug is that once you call std::vector::erase on a collection, all iterators (and const_iterators) into that collection become unusable. The Standard terminology for this is that erase invalidates iterators. (The reason for this is that std::vector behaves basically like a big heap-allocated buffer, and calling resize on the vector is allowed to do the equivalent of realloc⁽¹⁾ on the buffer, and calling erase is allowed to call resize (because if you erase half the elements in the vector, you're probably expecting the heap-allocation to shrink accordingly).)

So, what you're trying to do won't work using that naive for-loop approach. What you need to do is use a standard algorithm, namely remove_if:

#include <algorithm>

auto predicate = [](const File& f) { return f.ShouldBeErasedOrWhatever(); }
auto newEndIterator = std::remove_if(this->files.begin(), this->files.end(), predicate);
this->files.erase(newEndIterator, this->files.end());  // erase everything after "newEndIterator"

Replace f.ShouldBeErasedOrWhatever() with whatever your "..." is in the original code. Now you have valid, idiomatic C++11 that does the right thing — with no bugs!

⁽¹⁾ – Note on "the equivalent of realloc": Of course it's not really realloc; it's really a type-safe process that calls move-constructors and destructors as needed. vector knows it's not generally safe to memcpy arbitrary objects in C++.

Question 2

Assuming your example code is incorrect and it really is files.erase(it), then const_iterator version was only added in C++11 which it looks like you don't have since you're not using auto.