Popper was prepared to allow a little dogmatism to persist with a theory that appeared to be in trouble with anomalies.
Bartley wrote that this did not need to be described in terms of dogmatism, instead we would just accept that the theory was problematic due to the adverse evidence and we could keep working on it in case the issue could be resolved. The point is to acknowledge the problem.
Actually Popper had that based covered in his interview with Bryan Magee in Modern British Philosophy, Secker and Warburg, 1971
Magee: What happens if we can’t find a satisfactory successor to the refuted predecessor-theory?
Popper: Then we would, of course, continue to use the old refuted theory until a better theory was found; but we should use it with the knowledge that there was something wrong with it. There would be an open problem, and we should know in advance the minimum conditions which a new theory would have to meet in order to be regarded as an interesting solution to this open problem.
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