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I think you're imagining a problem which cannot follow from the practices of egg and sperm donation. First of all, the few bits of serious research on the subject have shown that the incidence of serious genetic problems in children whose parents are very closely related is quite miniscule. Full siblings have the highest incidence, but still very low. Half-siblings and first cousins have rates that are negligible. I don't think there's been any empricial research (probably for lack of a large enough verified sample pool) of the offspring of parent-child sets of parents.

On top of that, the only incidences of widespread genetic problems have been in very small populations which interbred almost exclusively for many, many generations. That's simply not what's going on with egg and sperm donation. These aren't members of insular groups like the Saudi or Russian royal families, or of insular cults like the Mormon polygamist groups. Nor are the same egg and sperm donors being used across generations -- there's a very narrow age range accepted for donation through any remotely reputable agency, and most individual donors donate for a much shorter segment of their lives than the official age limits (i.e. men usually just for a couple of years while in college or grad school, and most women donate only once and few donate more than a handful of times.

Furthermore, genetic testing is fast approaching the point where people can easily check for genetic problems before having children, and an increasing number undoubtedly will. I recently read an article about an ultra-orthodox Jewish community, in which the rabbi normally must approve all marriages before they happen. Due to the high incidence of serious genetic diseases in this population (e.g. Tay-Sachs in particular), which is due in large part to being a small, insular, multi-generational interbreeding group, there is an increasingly popular voluntary service in which young men and women of marrying age have themselves tested for the common diseases, with the results being held confidentially (even from the testees), and shared with the rabbi only when a couple is being proposed for marriage. The rabbi then nixes the marriage if both parties are carriers for the same disease -- still with nobody but the rabbi and the testing agency knowing what disease(s) the parties were carriers for, or even if that was definitely the reason the rabbi nixed the marriage.

Problems caused by technology are usually quickly solved by technology as well. One enterprising adolescent boy tracked recently tracked down his sperm donor father through a combination of his own DNA test results, and online genealogy oriented DNA databases, and the very skimpy personal info normally provided to purchasers of donated sperm (e.g. ethnic background, major physical characteristics, level of education and major, number of siblings, etc.). The kid actually only directly found a close relative who had registered on a DNA database for genealogy purposes, and contacted that person, who checked with the actual donor (maybe checking with a handful of relatives who might have been sperm donors), who then agreed to be identified and meet the kid (probably quite proud of what a smart kid his genes had turned out).

Your worry is no more statistically well-founded than a young adult who knows he/she is adopted being worried that his/her prospective spouse might be a sibling or half-sibling. Yes, it COULD happen, but it would be so rare, and the chances of any serious negative consequences so tiny even in the rare cases it does happen, that nobody should be losing any sleep over it.