I work as a CPA in the US here's how sales tax is generally monitored.
Credit card agreements-typically there are sales statements and annually, the credit card processor will release a form stating how much in credit card sales were made (separated by month). This is used for federal income tax reporting but can be a secondary statement for sales tax collections.
Cash collections-this is complicated. US tax authorities run into the same problem of figuring out cash revenue.This is resolved by requiring receipts to state "cash" or "credit" upon receipt of payment. A cash receipt will still get recorded, it will just have one less copy typically (since credit cards require charge slips). You could use consumers to do the job for you by starting a public campaign "ask for a copy of the receipt". If the receipt has the tax on it, then the business owners will be forced to do their job. It also gets buy in from the public.
You also need to give incentives for making accurate sales tax payments. Sales tax forms should be provided to each small business owner with a list of the items subject to sales tax, their rates, with no doubts as to taxability. Accurate and timely sales tax payments can be facilitated with an "on-time filing and payment" discount. Reduce the discount over 3 years, then for the two years after that institute increasing late payment penalties which cap at 10% of the sales tax due.
