Yes. Here are what I see as a few of the major problems currently faced by evolutionary psychology:
1. Evolutionary psychology is attempting to elucidate the functional organization of the brain even though researchers currently cannot, with very few exceptions, directly study complex neural circuits. This is like attempting to discover the functions of the lungs, heart, etc., without being able to conduct dissections. Although psychological evidence indisputably reveals that cognition has structure, it is less clear that it does so with sufficient resolution to provide convincing evidence of functional design. Can the current state of the art in cognitive psychology successfully cleave human nature at its joints? Maybe, maybe not. Despite these reservations, it is worth noting that virtually every research university in the world has a psychology department. Grounding psychology in an explicit framework of evolved function cannot help but improve attempts to unveil the workings of the brain. It is far easier to find something if you have some idea of what it is you are looking for.
2. The domains of cognition proposed by evolutionary psychologists are often pretty ad hoc. Traditionally, cognitive psychologists have assumed that cognitive abilities are relatively abstract: categorization, signal detection, recognition, memory, logic, inference, etc. Evolutionary psychology proposes a radically orthogonal set of 'ecologically valid' domains and reasoning abilities: predator detection, toxin avoidance, incest avoidance, mate selection, mating strategies, social exchange, and so on. These latter domains and abilities are derived largely from behavioral ecology. Although mate selection surely involves computations that are fundamentally different from predator detection, it is not so clear that the organization of the brain just happens to match the theoretical divisions of behavioral ecology. The concept of 'object' is obviously quite abstract, yet it is equally obvious that it is an essential concept for reasoning about mates, predators, kin, etc. The same goes for other 'abstract' abilities like categorization and signal detection. Ecologically valid reasoning about domains such as kinship may require cognitive abilities organized at higher levels of abstraction like 'recognition.' On the other hand, numerous experiments show that reasoning can be greatly facilitated when problems are stated in ecologically valid terms. Negating if-p-then-q statements becomes transparently easy when the content of such statements involves social exchange, for example. The theoretical integration of more abstract, informationally valid domains with less abstract, ecologically valid domains remains a central problem for evolutionary psychology.
3. Evolutionary psychology (and adaptationism in general) has devoted considerable theoretical attention to the issue of design, the first link in the causal chain leading from phenotype structure to reproductive outcome, but has lumped every other link into the category 'reproductive problem.' This failure to theorize about successive links can lead to spectacular failures of the 'design' approach. Three examples: 1) evidence of design clearly identifies bipedalism as an adaptation, but what 'problem' it solved is not at all obvious, nor does the 'evidence of design' philosophy provide much guidance (though more detailed functional analyses of bipedalism are further constraining the set of possible solutions). 2) Language shows clear evidence of design, and there are several plausible reproductive advantages to having language, so why don't many other animals have language? 3) It can be very difficult to determine whether simple traits are adaptations simply because there is insufficient evidence of design. Menopause may be an adaptation, but it has too few 'features' to say based on evidence of design alone (some 'features' of menopause, like bone loss, seem to indicate that it is not an adaptation). Very simple traits will not always yield to a 'design analysis, ' simply because there isn't enough to grab onto.
4. Evolutionary psychology is founded on a model of ancestral human reproductive ecology (the EEA), yet the current version of this model is woefully out of date. Life history theory, the sub-discipline of biology devoted to understanding the fundamental aspects of the reproductive ecologies of plant and animals, has made enormous strides in the last decade or so. Little of this work has entered the 'mainstream' of human evolutionary psychology. Part of the problem is that the units of analysis for life history theorists (e.g., body size, mortality rates, taxonomic categories) are quite different than those used by adaptationists (e.g., strategies, design elements). Yet life history arguments are central to much work in evolutionary psychology (e.g., parental investment). Evolutionary psychologists need to get up to speed on the current state of the art in life history theory.
Hunter-gatherer theory is a related issue. Evolutionary psychology uses an odd mix of Kalahari and tropical Amazonian ethnography for its basic model of the EEA. Although much (if not most) work by evolutionary psychologists relies on indisputable features of the EEA such as women got pregnant and men didn't, it is time for evolutionary psychology to start talking more seriously with archaeologists and paleoanthropologists. We know a lot more about the past than we did even 10 years ago, and some of what we thought we knew has now been called into question.
5. Convergent evolution vs. phylogenetic inertia. In contrast to early approaches to the evolution of human behavior that emphasized chimp or gorilla models, evolutionary psychology relies heavily on convergent evolution type arguments. The emphasis is on functional design, with little attention paid to traits derived by descent from recent and not-so-recent ancestors. Birds are as likely to be used as models as are baboons or bonobos. Functional arguments also typically pay little attention to phylogenetic constraints. Although it is not exactly clear what kinds of constraints human ancestry might place on human cognition, it surely places some. A synthesis of primate cognitive ethology and human evolutionary psychology that takes into account both the convergent evolution of similar psychologies in response to similar ecological problems, as well as phylogenetic history, has significant potential (as most primatologists would argue, I think).