The rim of BoE dollars "should" be plain. They used plain collars to enclose the Spanish dollar as it was being overstruck. In some cases, remnants of the original box-and-circle edge can still be seen, but only remnants.
I recall I had the same "that looks dodgy" reaction when I first saw the edge of a Bank dollar for sale in a local dealer here and was reluctant to pay the rather high asking price. He let me have it at a discount (since he wasn;t entirely sure, either) and I asked around at my local coin club; they verified with their own examples that the edge is indeed supposed to be plain.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis