My 1-year-old son sometimes wants to play with sophisticated things such as a laptop, headphones, a mirror etc. If I deny him those, he starts screaming and crying. Is it a good idea to subside and give him that with supervision? If not, what should we do?
Toddlers cry when they don't get what they want. They don't have any other way to express themselves. Giving them things that might be dangerous for them is generally not a good idea. Giving them things they might break usually isn't either, mostly for your own sake. So I would advise against giving them things that are sharp, fragile and/or expensive.
Instead, console the child (pick them up, hold them, talk to them) to calm them down and then distract them with something else. Usually the child will immediately forget that it wanted something specific and just go and play with the new object. If not, move the thing out of their sight and they will forget about it.
Note also that if the child constantly wants to play with whatever you are holding, they probably just want attention, not the thing you have.
1 year olds will, inevitably, want things that they can't have. They'll want everything, just to experience and see what it is, what it can do and if it's fun.
If they get denied that, don't like something in general or want to communicate then their sole way of expressing it is to cry about it.
Is it a good idea to subside and give him that with supervision?
I think the majority of parents out there would respond with a pretty immediate "No"- with some things, sure, but others? A solid, concrete, no. 1 year olds aren't in any way intended to be poking and prodding at things not designed or intended for them, this is for their safety and developmental benefit as much as yours.
By all means, if there's toys or products intended for them, let them go for it- but unless the Tablet is built to withstand all the punishment they'll give, you'd want to be supervising, yes. I wouldn't say it's best judgement to necessarily let them get used to entertaining themselves all the time with gadgets though, for obvious reasons!
As you'll find, they'll forget remarkably quickly if you distract them with something else, or hide/put away whatever it is that they're after. They may still cry and fuss over it, but letting your 1 year old get what they want every time they make a fuss isn't a habit you'll want to get into either!