Falsified student signatures in class attendance list I am required to keep a tag at the students' attendance of classes by the rules of the university where I teach. The students' attendance cannot be lower than 75% of the classes, or else they automatically fail the course. To do so, I am required to handle them a signature sheet in each class. I am also expected to keep this sheet as proof I really taught the said class. (Not that I agree with this system, but the director can inquire a teacher and they must be ready to present this "proof", so I must abide by this rule.) 

I have already come to terms with the fact that this is not really evidence of the students' attendance: they come late, leave before the class is finished, sign the sheet, and that's fine. However, even so, there are many absences and there is also the case of those students who falsify their classmates' signatures. I have already warned them on the first day of class that that won't be accepted, but in some cases the warning went unheeded. 

The question is, I've had experience that the directors will also doubt the veracity of the attendance sheet, possibly accusing me of being too unyielding and uncompromising, even hinting that I must have falsified the whole thing with evil intentions. Because, according to the directors, a significant majority of the students must pass, regardless of their efforts. I have tried to be more "accepting" of absences (mainly if the student has good grades), but I cannot swallow having to condone falsified signatures. Should I follow the "culture" of the faculty that don't care the least about this fact (attendance and falsified signatures), despite their own rules? Or should I follow the rules and face the (possibly unpleasant) consequences?
The system you're describing sounds like a bureaucratic nightmare to me (both for the students and for you; these things generally go hand in hand). I would therefore sympathize with (and turn a blind eye to) students tricking their way through it to the extent that is necessary to let them focus on the actual work. It's sad that they are getting free lessons in forgery when they ought to be learning something more wholesome, but as long as they are doing the coursework without academic dishonesty (as in, homework plagiarism), this should not count against them. A class is not a test of conscentiousness.

If you want to push your students to attend the class, there are other methods that don't involve automatic failure, such as giving mild homework hints in your lectures.

[Extended from my comment.]