Is there a moral aspect to financial debt in Buddhism? If I recall correctly I've heard that one can not be ordained if one has debts. Is this just a practical rule to avoid ordaining people that run away from financial problems or does it also have moral aspect to it?

Answers from all schools are welcome.
If you have obligations like debt you might be forced to disrobe. You will not be able to do what you set out to do and any debtor trying to get hold of you will be doing bad karma. 

Also you cannot practice properly as you will be afraid of debtors getting hold of you. 

You and the Sanga will get a bad name due to your not fulfilling your obligation. This has a karmic implication towards people who might bad mouth the monk and the order.

This can be extended to other obligations also. 

Regarding being disfigured or disabled it is the latter reasons. Also you need all your faculties in good condition to effectively do Vipassana.