>Have any of you imported a car without getting a chance to see it?
Yes, depression Challenger, North Carolina to Western Australia. Blogged about it from beginning to end in 4ch /o/ Ausfag threads.
>Was it a big mistake or is it something that seems like a bad idea but really isn't?
Yes, because I didn't know what I was doing and I did it solo like a total champ. It can be a great idea if you cover your bases and do it right and protect yourself.
Get it right and it's awesome. Get it wrong and it's a mess.
Before we begin, it's older then 30 years, yeah? Almost certainly. Just checking. Life gets a lot harder when your vehicle is younger then 30 years old and is imported.
Also make sure it has a title and that you get a bill of sale. Some American states don't believe in titles for old cars. No idea what you do then.
First, try to make sure you have a friend locally to help you with this. I don't mean a friend of yours, but a trustworthy contact who is passionate about the brand (preferably) or classics (at least) and has imported before or knows or has helped people import. Worst case, get your dad or something. It's better then nothing and having someone to keep you in check when you're in the thick of it is useful.
Next, research the car. Learn about it, it's common problems, what to look for, etc. Cruise forums dedicated to it if you can. Going in green with some book smarts is better then going in blind. At least skim the workshop manual. I downloaded mine and printed it at Officeworks. That was useful.
Now definitely get a few mechanics (I used two) at its location (GRORIOUS NIHON) to look it over, test drive it and take photos of things that need attention (do get a report on how the car is, stupid things you might not know of will trip you up when registration comes along (think window defoggers, etc) (also consider hidden costs like tires)). Good luck, I only had to deal with the Australian/American English divide.
Now, if you can, take what you got from those mechanics to someone In The Know where you are (ideally, someone who registers cars, a certified engineer would be ideal), and hash out a rough costing together of all it might need (be generous and add a few thousand in case of disaster here). If this is not possible, make a worst case list anyway and maybe consult a dedicated forum or cross your fingers. That disaster fund will be appropriate regardless.
I also recommend consulting someone who has experience with getting unregistered imports registered. It's harder then you'd think, but much easier with help.
After all that, if the price looks reasonable and you think it's viable, go ahead and bite the bullet. At this point brace for any relevant customs bullshit (I got charged a few hundred to degas the air-conditioner by my shipping company (fair enough?), and was "chosen" for "random" car cleaning, which is basically a flat fee on top of customs inspection that they hand out liberally. Suffice to say I found spiders in my car after this so assume your car won't actually be cleaned).
5K is a good deal thus far even assuming it's not perfect. You're not too deep in it if it goes belly up. I paid 11K for mine, and then 4K for shipping from Florida (inc. trucking to depot), for reference.
All that said, I still love my car, very, very much, but it's a project instead of a perfect Sunday cruiser when I could have got the latter. That's annoying, but I've gotten over it. Pic related.
Also, is that some Mini variant? Looks like it. You might want to talk to British Leyland Drift Champion in 4chan's /o/ in Ausfag threads. He's a swell guy, real nice, and is familiar with the brand. Tell him I said hello if you do.