To what extent are correlations of father's age with birth defects and autism causal?
This is a partial answer suggesting a possible causal mechanism.
One of the factors leading to birth defects and autism is mutations in the parent's genetic material. In a recently published article, Sun et al. (2012) observed that:

The paternal-to-maternal mutation rate ratio is 3.3, and the rate in fathers doubles from age 20 to 58, whereas there is no association with age in mothers.

In other words, while the mother's age will not have an effect on the number of mutations passed to the offspring, the older the father the more mutations. That means a possible causal mechanism for correlations of father's old age is an increase in the number of mutations (most of which are neutral or detrimental) passed to the offspring.
Kong et al. (2012) explain the connection of de novo mutations (of the sort observed by Sun et al. (2012)) to autism and other disorders more clearly. This blog post suggests why fathers might produce more mutations:

The difference probably comes from the distinct biology of male and female reproduction. Cells that give rise to sperm cells continuously divide throughout a man’s life while cells that develop into ovules stop replicating when the woman is still a fetus. Consequently, an ovule at any time of a woman’s life will have gone through 24 cell divisions while sperm will be at about 200 divisions in a 20 year old man and up to 600 in a man of 40 years. When cells divide, they replicate their DNA to transmit a copy of the genome to each daughter cell but this replication is not 100% accurate. With each division mutations creep in the DNA so the more divisions a cell goes through, the more mutations it accumulates.

References
Kong, A., Frigge, M.L., Masson, G., Besenbacher, S., Sulem, P., Magnusson, G., Gudjonsson, S.A., Sigurdsson, A., Jonasdottir, As.,   Jonasdottir, Ad., Wong, W.S.W., Sigurdsson, G., Walters, G.B., Steinberg, S., Helgason, H., Thorleifsson, G., Gudbjartsson, D.F., Helgason, A., Magnusson, O.Th., Thorsteinsdottir. U., &amp; Stefansson, K., (2012) Rate of de novo mutations and the importance of father’s age to disease risk. Nature 488: 471-475.
Sun, J.X., Helgason, A., Masson, S., Ebenesersdóttir, S.S., Li, H., Mallick, S., Gnerre, S., Patterson, N., Kong, A., Reich, R., &amp; Stefansson, K. (2012) A direct characterization of human mutation based on microsatellites. Nature Genetics [press]