For all our problems, our differences, we are together as of old.

【翻译】尽管我们有这样那样的问题，尽管我们有许多分歧，但我们仍然一如既往团结在一起。

for 在这里表示让步，常与all连用，相当于in spite of。

as of old 是个习语，意为“照旧；一如既往；一如从前”，在句中用作状语。又如：

People have splendid life as of old when they do the right thing at the right time! 人们在适当的时间做适当的事，照样可以活得精彩!

Will your love as of old prove true? 你的爱是否依然是真实的吗？

I could see that as of old their house was a port of call for all the lonely and the lost of the district.  我能看到他们的家依旧是那个地方孤独的和无家可归的人的避风港。