Realistically, if you're randomly audited you're not going to have any problems if the value of all of your donated items at a place such as Goodwill etc. is a few to several hundred dollars, receipt or not. Anything over $1,000 and I would definitely want to have a receipt. Those 18-wheel trailers are often unattended, but you can drop off goods 24/7/365 and wouldn't receive a receipt, so it's not uncommon at all not to not have written proof. Worst case scenario if you deducted an amount such as that is that you'd be forced to remove the deduction if you were audited and couldn't provide a receipt, but the odds of being audited AND being forced to remove the charitable deduction are probably about a million to one.
