From what I understand (I never had an RESP but would consider one for a future child), with the right type of withdrawal, you can use the RESP money for anything education related.
Basically, know that the RESP is considered to have three compartments within it: (1) your contributions, (2) contributions from the government through the Canada Education Savings Grant (CESG), and (3) the return on the investment, or accumulated earnings. The government contributes an extra 20% on top of your contributions annually by way of the CESG, up to a $500 max.
As you noted, official tuition fees, reported on a fee slip, is where one large chunk of the RESP will go. This will be pulled out of your original contributions and is known as a Post-Secondary Education (PSE) Withdrawal. Different RESP administrators (bank, discount brokerage, etc) determine what sort of proof of enrolment would be required, but it ought to be similar between them and different educational institutions. This withdrawal is not taxable by either you or the student, since the contributions were made with after-tax dollars.
Educational Assistance Payments (EAPs)
EAPs are for other expenses that the student would incur by being at university. In the first 13 weeks of studies, you can request up to $5000 in EAP withdrawals (full-time studies, $2500 for par-time), after which there is no limit. Each EAP payment is made up of the CESG and accumulated earnings portions of the RESP, whose proportions are determined based on the EAP amount. This is considered taxable income for the student, or beneficiary, in the year the EAP withdrawal is made.
It gets a bit fuzzy here, from my understanding. The student would ostensibly be able to purchase anything that they could rationalize as education-related, and I'm not sure what sort of proof different banks would need. Maybe just the confirmation of enrolment is enough.
This is the part of my post that should directly answer your question which, using this terminology, boils down to what sorts of expenses can I use the EAP withdrawals for? To this, from what I've read out there, I would say that you could probably purchase anything. From the student's point of view, they are enrolled in a qualifying education institution, and if they don't spend the money on education-related purchases, money required for those purchases will have to come from somewhere else anyway.
Any other type of withdrawal is like walking through a minefield. You can withdraw the original contributions without paying tax on them, but you would need to pay back the corresponding CESG back to the government. Other types of withdrawals would be taxable and may incur a 20% penalty. I don't have any more details on that.
As I mentioned, this is from what I've read and looked into for future RESP purposes. A new concept that has popped up is RESP vs TFSA. The TFSA provides the same tax shelter (after-tax dollar contributions, no tax on the gains), but also allows for no tax on the withdrawals. To add to that, the TFSA withdrawals are tax-free as well. The main benefit that the RESP offers that the TFSA doesn't is the CESG. My current opinion (and I could be wrong) is that you should contribute $2500 annually to the RESP in order to get the $500 max CESG, and anything else that you'd like to contribute should go in a TFSA. But I digress.
Hopefully my long-winded response makes some sense. Enjoy.