Admittedly I am a fan of Paleolithic continuity but I try to visualize also the opposite view and listen to the arguments in favor of it. But in the end I always come back to the Paleolithic continuity model, even if I also reckon it may pose some further questions - interesting questions in any case.
Basically the main reasons why I end up returning once and again to the mainly Paleolithic origins model are two:
1. Archaeology: the expansion of Cardium Pottery shows much more often than not, signs of cultural assimilation of the natives; most CP sites include (side by side with the typical pottery, signs of farming and apparently domestic animals' remains) local Epipaleolithic stone tools. Maybe the dates of Neolithic arrival have been pushed back slightly in the last decade but the nature of the sites remains the same.
2. Genetics: specially mtDNA seems solidly dated to Paleolithic times in most cases. Additionally, the structure and geography of mtDNA H and Y-DNA R1b is so much alike that they seem to require the same explanation. Also it seems very odd that there would be no (absolute zero) Y-DNA remains of Paleolithic peoples somewhere in Atlantic Europe at least (which would be the case if R1b was of Neolithic origin).
But I have always felt somewhat weak in the technical (amost esotherical) formulations, most of the time only used to speculate on age estimates based on the quite unrefined molecular clock hypothesis.
Luckily I have now found this 2005 paper by M. Currat and L. Excoffier, that abounds in this problem precisely from the technical point of view: The effect of the Neolithic expansion on European molecular diversity.
Read it, please: it is most interesting in spite of the mathematical focus. Their most important conclussion is that the only way that it could be less than 50% Paleolithic component in the overall European genetic pool, would be that all 100% of it would be Neolithic, an option that does not seem acceptable under any light.
These results imply that, under our model of a progressive range expansion of Neolithic farmers with possible genetic exchange and competition with local Palaeolithic hunter–gatherers, it is very unlikely that the Palaeolithic contribution be globally smaller than 50%. If that was the case (e.g. Chikhi et al. 2002; <30%), it would imply that Neolithic would have had virtually no genetic contact with local populations, like under a pure DD model. Global surveys of mtDNA molecular diversity (Richards et al. 1996, 2000), and the simulations of mtDNA mismatch distributions argue against such a low contribution of Palaeolithic populations to the modern gene pool. Indeed, examination of figure 4 reveals that in the absence of exchange with hunter–gatherers, mismatch distributions should often be multimodal, and have a mode closer to zero in populations sampled far from the Neolithic source. On the contrary, most European mismatch distributions are smooth and unimodal (Excoffier & Schneider 1999), and the mode of mismatch distributions is quite homogeneous across Europe (Excoffier 2004), as expected when the contribution of Palaeolithic lineages becomes important. Moreover, previous dating of demographic expansion for European populations has pointed towards 40000 years ago or more (Comas et al. 1996; Excoffier & Schneider 1999), in keeping with a Palaeolithic expansion.