For example, one wire of a twisted pair is longer than the other wire (imbalance starts from the middle of the twisted pair, everything is balanced before the middle point). What problems will it cause?
The inverted signal will be phase shifted compared to the non-inverted. If the imbalance is a significant portion of the wavelength, there will be noise issues. Noise is emitted because the EM fields of the signals don't cancel each other like they do on a matched pair.
For a diff pair, having a mismatch not only reduces the data eye pattern margin, but it also causes common-mode current for the uncancelled portion of the signal. This will show up as noise on the ground reference alongside the pair and can be a big EMI headache.
This is a huge problem for example with HDMI on the driver side: unequal trace length adding differential skew to the pairs, resulting in common-mode noise at harmonics of the data rate. One remedy is to apply common-mode diff filters to knock down this non-cancelled noise component.