I would suggest making sure the home inspection is done prior to applying for the mortgage. That way, you won't lose the non-refundable mortgage application (credit and appraisal) money.
I'd also watch the interest rates to see if you want to lock your rate or not. Rates seem like they're going up, so it may be worth it to lock it up now while you can.
If you are seeking financing, you need to make sure the lender has everything they need to approve the loan. You also need to send a copy of the contract to the closing attorney's office so they can do the title work, etc. You will need wiring instructions from the attorney if you are bringing money to the table. Other than that, I would be on site during the inspection. Get some insurance quotes. You will need coverage on the day of closing. If you are paying cash, it is much less complicated.
Thanks for the responses guys - I will act on all of it.