I would like to know what errors during the process of gene cloning can potentially lead to genetic instability, as it often relies on the precise insertion of a target gene into a suitable vector, and this process is not error-free.
You're going to have to narrow down your question.
Putting a piece of DNA into a plasmid = cloning
Putting that plasmid into an organism =/= cloning
You sequence the vector to see if the insertion is error-free, complete, and in the correct orientation. It's very often error free, but it's good to check to be sure. It is *easy* to get precise insertion of a target gene into a suitable vector.
Not sure why you think this would cause "genetic instability" since a plasmid is just a piece of DNA.
Now, Agrobacteria-mediated T-DNA mutagenesis does cause genetic rearrangements (translocations), but they are heritable and stable. The double-stranded breaks & repair happen just once.
Go chat with your advisor to clarify the boundaries of your question.