If we do leg exercise with wrong posture than it could lead to back problems and there are exercises in which slightest mistake can lead to back problem.
There are many leg exercises which can lead to back problems like squats and deadlifts, but if those are executed with proper technique than there will be no issue.
Leg extension is the exercise which involves more risk of damaging your back even if executed with almost proper technique. Another exercise is hamstring curl which can also cause back problems.
While doing hamstring curl when we start to lift heavier weight or when we get fatigued we start to lift our butt into the air. In some cases we even start with our hips in elevated position and that is worse posture for our back.
Problem is that we have to get our heel to our butt and when we can't bring our heel to our butt we try to get our butt to our heel. When we lift our butt in the air we shorten the distance between our hips and our heels however we loose the correct posture and this could become the cause of back injury.