The BBC iPlayer app and beta web site (no app required) work just fine in the UK, but will not work in other countries. This is simply a restriction placed on the BBC because UK residents have to pay a licence fee to the BBC and it would seem unfair to them to allow non-UK viewers to gain access for free.
However, the BBC are working on a subscription-based iPlayer service that will be available in the near future - probably within a few months. Meanwhile, some BBC TV programmes are available in the iTunes store for download and viewing in the iPad's Video app - though the selection is pretty limited at present.
In addition, the present iPlayer app is a streaming-only service and for many, even in the UK, where broadband coverage is limited, this can be a problem. The BBC are also working on an undated iPlayer app that will enable programmes to be downloaded and viewed off-line, to overcome this problem. Of course, streaming will still be available as it's clearly more convenient if you have a good enough broadband connection to support this. Also, the present iPlayer app won't allow streaming over 3G, which is a real pity for people like me who have a great mobile broadband connection and an unlimited data plan but a rather poor cable broadband (I live in a rural area, but cell coverage in the UK is very good). The BBC have also said that future iPlayer apps will allow streaming over 3G although whether they'll be able to persuade Apple to relax their 20 MB download limit for 3G is another issue altogether...
Tim
Scotland