According to Rafael Yuste, there are eight:
1) Classifying all neuronal cell types, preferably using quantitative measurements. One huge step towards this goal is the new ability to use transgenic animals where certain cell types are labeled genetically. It is next to impossible to reverse engineer a system without knowing the parts involved.
2) Deciphering the basic synaptic microcircuits of at least some areas of the brain. This would help reveal the actual structure of neural connectivity.
3) Discerning general computational and logically strategies of circuit algorithms in different areas of the CNS or across species. There is not much current effort towards this goal but it could be useful in enlightening some of the general strategies natural selection has used to get from circuit to behavior.
4) Understanding the large scale dynamics of neural circuits and build upon the work done recording from individual neurons. This could help us understand spontaneous activity in the brain that is seemingly uncorrelated to sensory inputs.
5) Monitoring group levels of neurons with new cell imaging technologies. He is particularly fond of calcium imaging. Although the technology is there, it needs to be improved upon and become more widely adopted.
6) Selectively activating or deactivating certain neurons. The ability to test a single component at will is very useful for engineers, and it would be a useful step in deciphering neural activity. Boyden and Deisseroth have developed such a technique in blue and yellow light activation, detailed here, but it needs to be refined.
7) Illuminating the connectivity of neurons at synapses. There are a number of technologies poised to accomplished this (novel ultra-structural methods, glutamate photo-stimulation, or viral and genetic approaches), but one needs to be vastly upgraded to lead to the “promised land.”
8) Scaffolding experimental work with more concrete theory. There is some promise here in circuit attractors, information theory, Bayesian coding, and temporal multiplexing, but there is clearly much more mathematical work to be done.
Yuste R. 2008 Circuit neuroscience: the road ahead. Fronteirs in Neuroscience 2:6-9. Pdf available here.