Let's say you're a 23-year-old man who impregnates a woman. Will your genes be the same if you were to impregnate another woman at age 35? Will your genes in those 12 years have changed/mutated/become smarter?
Answer
Yes, there are some differences between the gametes that a parent produces at different ages!
Mutations in the germline during mitosis
Every time a cell replicates some mutations may occur (even through mitosis). Of course, any mutation that occurs in cells are located in your hand or in your brain, for example, will not be transmitted to the offsprings. Only mutations occurring in the germline (cells in the testis and in the ovaries whose descendent or themselves go through meiosis) are possibly passed to the offsprings. Interestingly, because of the developmental pathways of sperm cells and ovules, sperm cells go through a lot more mitosis than ovules do, resulting in more mutations in the sperms than in the ovules. Therefore, if you look at a mutation in an individual and assuming you know that the mutation occurred during the lifetime of the parents, then you are more likely that the mutation comes from the father than from the mother.
As reviewed by Cochran and Harpending (2013), mothers transmit on average a number x of new mutations to their offspring. This number x is independent of the age of the Mother. Fathers, however, transmit a number of new mutations to their offsprings that is very much dependent on the age of the father for developmental reasons.
Of course, as it has been pointed out there are various environmental factors that may increase or diminish the mutation rate (such as the mutagens (Tobacco, X-ray, ..))
Note on the process of adaptation
It is important to know that a vast majority of mutations are deleterious (impact negatively the reproductive success and survival of the individual carrying it). If we assume that no selection occurs between the cells of the germline, then no adaptation is possible. And in average sperm cells of an old guy should have lower fitness than the sperm cells of the same guy when he was younger. This process is referred to as mutation accumulation (mutation accumulation is not a concept that is specific to somatic lines mutations). However, one may argue the opposite! One might think that the cells that carry the new mutations (the mutation that occurred during the lifetime of the man) may be selected for or counter-selected. In such a case, the few beneficial mutations might be enough to make our cell lineages more fit with age. Whether the fitness of cells increase or decrease through our lifetime is dependent on the effective population size, the mutation rate and distribution of mutational effects. One can calculate the critical parameters yielding to one (mutation accumulation and fitness decrease) or the other (fitness increase through age) thanks to the mutational meltdown literature.
It is important to note however that what increase the fitness of a cell might decrease the fitness of its carrier. Knowing the joint distribution of mutational effect for both the carrier and the cells should allow us to calculate if reproducing late in life allows transmitting better genes than reproducing early in life. Intuitively, I would expect that reproducing early in life would allow a parent to transmit better genes.
Epigenetics
We have to talk about epigenetics also. Epigenetics refers to all the modification that occur "around" or "on" the DNA but which are not the modification of the sequence of nucleotides. It is possible that the transmission of epigenetic modification is dependent on the age of the parents. But I have never heard of any case where this happens.
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