I think I may have done something wrong

Three days ago, I bottled a batch made from a Brewer's Best Irish Stout kit. The OG was 1.05. It was in primary for six days, secondary for two weeks. Throughout, I had trouble keeping a steady temperature. It started at around 66, but topped out at around 73. Most of the time it was on the high side. FG as measured before bottling was 1.02. It didn't seem right at the time, but I bottled it anyway. Now, I'm sweating it. Please advise, thanks.

It sounds like the issue is you racked to secondary too soon, and the yeast didn't have time to completely finish. You probably should have hit closer to 1.016 or something(not positive-but 1.02 is usually high-it will just be a little sweet). Was the gravity stable before you racked to secondary? You probably want to wait 2 weeks minimum before doing that next time, if you really want to secondary...but you'll find that a lot of people don't, unless they are adding some kind of fruit or spices or if they are doing long term aging. Should be fine. Now its time to get started on the next batch

Dont worry, thats a common fg with the bb irish stout kit. I brewed it up a month and a half ago with similar results. Bottle bombs probably arent in your future.

The malto dextrin pushes up the unfermentable sugars. Do you recall what yeast they gave you? If it was windsor, thats a moderate attenuating yeast and sometimes stops early, although 60% isnt great.

If its anything like mine the beer wont taste good for another month at which time it should be sweet but tasty. Just dont expect a big frothy guinness head without nitro. Enjoy!

I think the yeast was Nottingham, in which case 60% is low indeed.
I didn't take a gravity reading before reracking to secondary, I just assumed that it was ready based on past brews. Now I realize the silliness of this but at the time it didn't cross my mind.
The sample I tasted was pretty sweet and a little thin, but not unpleasant. At this point I'm not expecting it to wow me, I'm just hoping that I don't have to deal with exploding bottles.

I wouldnt worry. How much maltodextrin? Thats why its high maybe. If you went by priming sugar guidelines for stouts, they are generally the lowest carbonated beers so that should get you some assurance also. Stouts tend to take longer to carb up also so just drink one every week after a few weeks to check on carbonation, but chill the one to drink good beforehand. They can take longer to taste good also.

I did the same kit for my second brew. I did primary for two weeks and secondary for another two, my FG never dropped below 1.020. RDWHAHB

In general 1.050 to 1.020 could be a concern. From what everyone's saying about this particular kit, you are probably OK. In the future I would recommend you leave it in primary longer to make sure it finishes dropping gravity before transferring (if you transfer at all).