Judging from the enormous number of requests for survey participation I see on this forum, I wonder how many master's dissertations or even PhD theses are based on convenience samples of postgrad students? Which has implications for the reliability of the results.

I think lots of them are. My study needs a very specific group of people and recruitment has been slow and painful, and my supervisor has kept saying, 'it's a shame your study can't just rely on students'. I was actually surprised that this would be acceptable at PhD level because, as you say, it has huge implications for the claims that can be made about the results. It's a shame recruitment is such a sticking point - I get numerous requests by email each day to participate in studies.

I expect most of them are students. There must be some papers published on this somewhere!

My recruitment had a variety of people. I was focusing specifically on men in Australia, but while I would get more than 50 responses to my advertisements, only 20 men actually volunteered to be interviewed.

I would think that the study would be skewed by postgraduate student input, but if the surveys actually have an option to keep track of the demographics, you write about that and can use it to your advantage.

For example, everyone who participated in my study were Anglo-Caucasian. Which wasn't my intention, but those were the men who volunteered. So in my thesis I make a point to say that it is through an anglo-celtic lens, and therefore not representative of all men in Australia. I reflect on this and use this in my limitations, as well as in my conclusion when discussing future research avenues.

No data is 'bad' data, or at least in social sciences. It's about interpretation and framing of your results.