You check on the AI debts fairly easily. Click the declare war button on one of their allies, but don't actually declare. Where is says if they will join or not, it will show the AI's reluctance to join the war based on their debts. This will show their debts in absolute ducats. Also, their reluctance is based on debts relative to monthly income.
According to the wiki, each month of income worth of debt gives -2.5 (according to the wiki) reasons to join a defensive war. For reference, forced bankruptcy for 4% interest would happen at 300 months of income worth of debt, or a calculated value of -750 reasons to join from debt on a defensive war.
Also, in this patch, the AI can't handle mercenaries, keeping them around for years while deleting regular regiments. This can result in AI's being in debt despite never losing wars, or even fighting difficult wars.