Gene selectionism. The most basic argument for gene selectionism is that genes replicate while phenotypes are temporary so selection of phenotypes cannot by itself produce cumulative change. But this is a gross oversimplification. Not only genes replicate, for offspring also receive cell membranes (only membranes make membranes), symbiotic organisms, and other biochemical stuff from their parent. Also, one can imagine situations where there is accumulation at the phenotypic level without accumulation at the genetic level (when a trait depends in a complex way on several genes). Better arguments for gene selectionism exploit weaknesses stemming the conventional view's reliance on the organism concept. Gene selectionism avoids this problematic concept which lumps together many diverse things (complex animals, single-cell organisms, plants, colonial organisms such as corals, etc.). This perspective suggests questions which the conventional view obscures, e.g.: Why are there organisms (considerable investment to build a body)? Why are cancers not so common as to undermine the viability of organisms? There is also the "extended phenotype" argument: the traits by virtue of which genes are selected need not be traits of the organism in which they are contained. E.g.: there are parasites which kill their host but induce it to leave a sexually attractive corpse, whence they find a new host by causing this trait in their original host. One may reply: but it is not the extra-organismic trait that is being selected for but rather the organism's ability to create it. However: what matters for (or "is visible to") evolution is the ends not the means, the outcome not the ability.
Critiques of gene selectionism. Something seemingly not captured by gene selectionism: suppose certain organisms have either of the genes A or B for traits and either of C or D for behaviours; and suppose that AC and BD are successfull combinations while AD and BD are not. There seems to be selection for neither of the genes A, B, C, D, only higher-order entities. The gene people reply that this is explained by frequency-dependent selection (i.e. frequency or A vs. B influences selection on C and D, and vice versa). Selection is already relative to many things---why not other genes as well? But why then not reduce all the way down to the four nucleotides? For gene selectionism to work a gene needs to have a phenotypic effect (in order to be visible to evolution). Its proponents used to define genes as reasonably-sized chunks of DNA ("evolutionary genes"), because this went well with their view of cumulative genetic selection. But the connection with phenotype would then be so indirect and variable that genes would be virtually invisible to selection. A better gene concept is needed but not provided. Some have tried to start at the other end and define genes functionally in terms of their phenotypic effects; but to serve as the basis for gene selectionism such "genes" must of course have a reality independent of the phenotypes by which they are defined, which is far from guaranteed.
Priority of genes. As noted, much more than genes are being passed on to offspring; further examples: bird's song, nest site and material; "host imprinting" (e.g. eggs laid on a specific plant which hatched organism memorises). Perhaps one should think in terms of "developmental systems" instead of narrowly focusing on genes. Gene selectionists need to show that genes are privileged over these other factors. Their main proposal is: genes are the only thing that carry information (this has even been phrased as a redefinition of evolutionary genes). But this is hard to define in a satisfactory way. For example one may say: genes have a specific intention unlike other developmental factors. But intentionality is difficult to define and conceive of materialistically. One may try a teleosemantic definition: intentional content is about what evolution has defined it to be about. E.g.: a rabbit's fear of certain cues has intentional content: "there is a predator here". But this definition applies to other developmental factors as well.
Group selection. Group selection faces problems: often almost impossible to test empirically (e.g. that hierarchies exist to minimise wasteful conflict); there are often equally plausible explanations based on individual selection (e.g. alarm calling shows the predator that you are a difficult pray); susceptive to subversion from within (by e.g. non-altruistic individuals, who have much shorter generations than the group and so overtake group selection). An alternative is kin selection ("inclusive fitness" included kin) which has some empirical support, e.g. eusocial insects with queen structure whose genetic structure is such that non-queeen females are more closely related to their sisters than their daughter which explains why they help the queen instead of breeding. A more abstract alternative is trait group selection, which sees anything with a common fate (common causal trajectory) as an interactor; e.g. (im.), crickets paddling pairwise to cross pond. This view subsumes kin selection and reciprocal altruism as special cases. It need not be susceptible to subversion from within because trait group selection need not be slower than individual selection. Another view: population structure is part of the environment; altruism may evolve through selection for individual fitness given that the environment includes many altruistic individuals. This can also subsume previous views, but it can be criticised for not being explanatory, not accounting for the process only the results (same "averaging fallacy" as naive gene selectionism).
Adaptation. One should not assume that any successful trait is the result of specific selection; this would be to look at organisms as "mosaic of traits," ignoring interconnections. Developmental constraints (entrenchment) rather than adaptive value seems to explain why all mammals have almost identical ear bones. An alternative to adaptationism which does better at explaining this sort of thing is explanation by classification, in analogy with the periodic table of elements.
Human behaviour. It is difficult to study human behaviour from an evolutionary point of view for a number of reasons: relatives extinct; no invasive experiments; environment has changed; hard to identify trait units (has e.g. aggression evolved as one trait or several more specific ones?). Proposed evolutionary models of human behaviour suffer from weaknesses in addition to these. Evolutionary psychology (e.g.: male promiscuity and female coyness may be explained by their different investment costs in reproduction) is based on an adaptationist point of view and ignores the interactive character of social evolution (assumes fixed problems). Some have tried to apply evolution to ideas (ideas compete, replicate and evolve) but this ignores the fact that evolution depends on the rate of mutation being just right (also, evolution explains apparent design so why apply it where there is actual design?).