Below is a formal and polite equivalent (synonym) of 'problem' which you can use in your business or professional pieces of writing.
With this meaning, 'issue' can be used in exactly the same ways that you would use 'problem'. For some reason, if you use 'issue' it makes the thing which there is a 'problem' with sound less important/serious.
It is perfect to use when you have to inform somebody about or talk about a 'problem' which you or your business/organisation is responsible for. If you (or your business/organisation) are the person having the 'problem' and you want to complain about it, I would use 'problem' instead of 'issue' to make it sound more important/serious.
'I would like to make you aware that we are currently experiencing some issues with the delivery of your order.'