What's the difference between 互相 (hùxiāng) and 相互 (xiānghù), both meaning "mutual"?
I'd say 相互 adds a bit emphasis on the mutual effect. It may be because the reversed order draws more attention. E.g. 我们应该增进相互了解. 尊重是相互的。

互相 is more casual. e.g.我们应该互相学习. If you say 我们应该相互学习， you express a bit stronger necessity of learning from each other.