other people correcting your technique? your opinion?

I hate being critiqued...mainly because I hate when attention is on me. And sometimes feels like I am being criticized... That being said, I'd probably appreciate it in the long run - especially if it benefits me!

It all depends how you approach the person. You can always start with...Hey Try This. My boyfriend always tries to tell me to do something differently but sometimes I'm not at the level where I can handle it yet. He's a marine so he thinks he does it better, but at the same time I kick him out of the room cuz then by him talking I get kind of unmotivated. So some people might take it good and some people might take it bad. It really depends on the person.

If I was doing something really wrong that could potentially injure me, I'd definitely appreciate a head's up!

Me personally would more than welcome it. I am newer to lifting and love it, but I am accident prone and don't want to get sidelined with injuries. I think a lot of people would think it's rude though. With the little bit of knowledge that I have, I see people at the gym doing stuff that make even me cringe.

I am studying to become a Personal Trainer atm, and I see a lot of people doing things wrong at the gym...
eg people swinging with lat pulldown, swinging with bicep curls, people lifting their back up on the bench press whilst lifting the weight.

It all looks like an injury waiting to happen, but would you find it ignorant if someone came up to you and corrected your technique, cause you're scared they may hurt themselves or they will not be getting the most out of an exercise?

I never ever say anything to anyone with bad technique...However, I purposely shake my head at them when we make eye contact...I have been known to bust out laughing too...

Kills me when dudes put way too much weight on their lat pull downs and they are trying to use their whole body to pull it down...

or the habitual curl bar rocker...bwahahahaha

I don't mind as long as they truly know what they are saying. I've had people come up and try to "correct me" and give me terrible advice. I think if you started conversation and worked in a comment like "I was reading if you position..... more effective..." then they might be receptive to it. However, I can see a lot of people not liking it.

I would love someone to do this (especially if I was doing something that could result in an injury) but i can understand why you are worried about doing it - not everyone would take it well!

Honestly, unless you know them or they have hired you as their trainer.. I wouldn't say anything. I would find it annoying.

If i see someone doing an exercise incorrectly and I want to use the equipment next, I show them a "different" way of doing the exercise to "work" a different muscle group. In other words, I show them how to do it correctly without telling them that their way was wrong.

Some people might be open to constructive criticism from a total stranger; others might not take it so well. Once you become a personal trainer, it might be different then because they'd recognize you as a someone who works there, and a "voice of authority". But even then there's a fine line between that and being the "policeman of the playground".

I personally would love it if a personal trainer came up to me and said,I am so and so and I am a personal trainer here. I notice when you do this you do this. If you do it this way you will get better results and save yourself an injury.

Maybe its also in the approach. Making it more casual. But yes, there is always going to be someone who can't handle constructive free criticism. I would guess you would have to be prepared that some people might not like it, but if you can learn to read who is a newbie they would probably appreciate a professionals advice

Depends on delivery, content, and awareness..
delivery is self explanatory and has been covered already.
what I mean by content and awareness, is that the person recommending would need to know what movement you are doing, where you are on training cycle, objective, etc. might also relate to the depth of the training that the person recommending has. For example, what if you are doing a push press, but if they "think" you are doing a military press in a more traditional bodybuilding fashion, they would say your form was wrong and you were cheating. Same could be said about having an arch in back for bench.. would depend on how much arch and how much weight. If you are going fairly light you probably can be pretty flat, but if going heavy you will have some arch and if trained to power-lift will have more arch.

its all relative. I have had people tell me some CRAZY stuff over the years. I just smile and say thanks most of the time. I do get it more often if I am doing something they are not familiar with.. for example an SLDL

I think that if you are new trainer and continue to learn over the years, the advice you give in year one will be greatly different than in year 20 (possibly even directly contradicting the year one advice)

Don't be THAT guy at the gym:

http://youtu.be/_-91_iXATY8

you can use your back a little to cheat on curls and other movements as long as you know how to do it properly without injuring yourself. I see a lot of people doing wrong things but i also see a lot of guys cheating properly for the last few reps. I cheat on lat pull downs too when i can't go on so i swing around 2 reps. It will give the muscles an extra burn than just giving up.

If I truly am doing something wrong, I would rather have someone stop me and correct me then let me continue on and hurt myself.