Last spring I saved seeds from one of my broccoli plants. This was a somewhat risky exercise as broccoli plants must cross pollinate with another broccoli plant to produce true to type seeds. While I have had success in the past saving seeds from vegetables that cross pollinate it is doubly risky saving broccoli seeds is it is part of the brassica genus, which includes a large number of plant varieties such as cabbage, cauliflower, Brussels sprouts, Pak choi, mizuna, rocket and canola, to name but a few. Which means that there are a lot of potential plants in the average vegetable patch to cross pollinate with.
While in the past I have had success saving true to type rocket seeds they eventually cross pollinated with some other brassicas to produce odd shaped unpalatable rocket plants. But in the case of my saved broccoli seeds I did not get past first base. The plants that grew from these saved seeds only vaguely resembled a broccoli plant, displaying tiny heads and leaves of a lighter colour and of a different shape.
The reality is that if you want to save seeds from vegetables that need cross pollination to produce true to type seeds you must grow two or more plants covered with insect netting (to prevent bee pollination) and hand pollinate them. Otherwise, there is a significant risk that you will end up with mongrel seeds like these.

LEFT: Broccoli plant grown from the seeds I saved. RIGHT: True to type broccoli grown from commercial seeds.