What will happen if someone fits a linear regression on a 0-1 problem rather than to fit on logistic regression?

Basically linear regression uses straight line function but logistic regression uses sigmoid function .Below are the point of things happen during fitting a linear regression problem into a logistic problem.

1. Error terms will be large at the middle values of independent variables which is Xand small at the extreme values, which strictly violates the rules of linear regression assumptions that errors should have zero mean and should be normally distributed
   
2. It will generate nonsensical predictions of greater than 1 and less than 0 at end values of X
   
3. The ordinary least squares (OLS) estimates are inefficient and standard errors are biased
   
4. High error variance will occur in the middle values of X and low variance at ends
   

The below image can show how fitting of linear and logistic regression differ from each other