Other American countries where the USD is legal tender include Panama, Ecuador, El Salvador and Uruguay, and several others. Some allow it to be spent in shops alongside their own currencies, others have fully replaced.
These sort of arrangements can work, but are also an admission of failure. Running two currencies, only one of which you print, is a trap. People will swap currencies to save in the one they trust, constantly offloading the local one to get dollars. Full substitution is usually the result of absolute failure, it is very difficult to reverse, and it deprives the government of valuable
seigniorage income.
But it has a single clear advantage also. Which is that you pay your workers, tax your citizens, buy imports and borrow on the bond markets all in the same currency.
Maintaining a currency peg over the long term (like Hong Kong for instance which has been pegged to the dollar for 3 decades) is a blessing and a curse. It imposes similar fiscal constraints to those of currency union, and locks you into a consistently mis-priced currency. If you allow the stresses on that peg to build up, eventually somebody will massively short your currency and make you pay through the nose to defend the peg (remember the UK exit from ERM?) or break it.
Argentina used to peg to the dollar, but they never did so with the necessary restraint. If you try to maintain it by letting values slip out of reason and imposing controls on how many dollars people can buy, stresses build and the whole project fails. The important thing about a peg is that you have to make sure people are willing to exchange between currencies at a constant rate. If you force the issue through repression, that won't last. This has recently become an increasingly urgent problem for Argentina yet again, and is a major reason for Venezuela's slow motion collapse in penury.
The best solution in an ideal world is for Scotland to be brave. As a sovereign nation they should have their own currency and let it find its own price. The problem is likely to be that they are too tied into our economy, meaning their businesses will want to accept and be able to make payments in GBP without the costs and uncertainties of fluctuating exchange rates, and all the expensive hedging that requires.
As I haven't even heard the notion of a free floating currency mentioned, I assume that concern looms large, and therefore a peg seems unavoidable. One day they will probably walk away from a GBP peg and switch to the Euro. Unless we peg to that first.