Is it generally a good idea to use headphones in the production/mixing of audio?
And what can I do if my speakers are terrible (e.g. laptop speakers), and I'm on a shoestring budget?
The best course I can recommend is to use the best tools and resources you have available. Headphones are not ideal, but they're better than bad speakers, and probably better than even good speakers in a bad listening environment.
A lot depends on what you're mixing and what the target environment will be. Mixing music or voice that will mainly be consumed on earbuds is different than mixing for a concert venue, a movie theater, or a TV in a living room.
It is a good idea to avail yourself to as many different listening environments as possible. As others have mentioned, higher quality monitors and higher quality listening environments will allow for more precise control.
However, unless your end user will be listening in that same high quality environment, some of that precision will be lost to the listener.
If your media will be consumed on laptop speakers, it is a good idea to know what that sounds like (and perhaps make adjustments accordingly).
If your media will be consumed on headphones, it is a good idea to know what that sounds like.
Headphones as a sole means of production...? probably not. But then again, anything as a sole means of production... probably not.
While I agree with Jim, to use the best tools you can, I always recommend headphones, if for no other reason to isolate what you're recording from the background noise. You have no idea how many times I've not heard the applicance running in the background until I had my headphones on. Alternately, you may hear a lawnmower outside, but only upon wearing headphones will you realize that your mic isn't even picking it up.
When it comes to mixing, a lot of the craft is to interweave the subtleties of each track. Without headphones, a lot of those subtle details may get lost.
Shoestring budget-wise, save your pennies and make the investment. Even a cheap, $7 pair of earbuds will help you isolate unwanted noise from your recordings and help you hear the subtle dynamics of your mix.
Those considerations are so important to making good audio, that I'd recommend borrowing headphones or earbuds from someone until you can invest in a decent set.
I use headphones for stuff like late night tracking , mobile production but will always check my tracks on a good pair of speakers in the morning
Sennheiser HD25 series are the bare minimum IMO
Headphones are great to get into production but you will need a pair of decent speakers sooner rather than later .
A mid range pair of Hi Fi speakers will be enough to cover your needs .
A lot of knowledge and information can be found at sites like gearstlutz.com and KVR
This reply is dependent on how serious you are about it if you are just looking to mess about with audio on the weekend etc none of these answers matter just use what you got or can afford to get