I came across a very interesting explanation of what actually happens in an incident such as the one which felled the LHC, from Vern Paxson, firstname.lastname@example.org. He worked on software for the 1980s big science experiment, the Superconducting Super Collider - and has kindly allowed me to quote his description of what the "bad electrical connection" actually was. Over to you, Vern!
"Bad electrical connection" is a layman's explanation of what accelerator physicists refer to as a "quench". This is in fact a routine event when working with superconducting magnets: somewhere something in the winding is imperfect, such that, when under the influence of extremely high magnetic fields, there is physical motion in the magnet's wire, leading to friction.
The friction generates local heat which transitions a small amount of wire from superconducting to "normal". The magnets carry such immense currents that the small resistance of the normal wire turns into a large amount of local heat; this in turn *transitions more wires* from superconducting to normal; and the process spreads.
It all happens fast, with the risk of explosion.
To counter this threat, superconducting magnets have high-speed circuitry designed to detect the onset of quench events. When detected, they very rapidly (and counter-intuitively) heat up the entire magnet, causing it *all* to go normal. The goal of doing so is that while individual wires can't possibly bear (when normal) the heat of the amperage going through them, the entire magnet has enough bulk volume to do so.
When a superconducting magnet is first commissioned, it undergoes "training", in which it is repeatedly (1) powered up to the point of quenching, (2) the quench-protection circuitry kicks in, (3) the whole thing goes normal and thus doesn't explode ... and (4) the imperfect winding that moved due to the high magnetic field is now in a new position where it likely won't move again (since the original motion was driving it towards such a potential-energy minima). Therefore, that particular quench won't recur. However, others might. So during training, you do this again and again until no more quenches occur.
So, Yes, such failures are expected, but in this case something went wrong with the quench-protection mechanism leading to the explosion. A bit more than just "a poor solder connection" (though clearly still not good, and I believe magnets are generally trained *before* installing them in the beam tunnel).
(Explanation/disclaimer: this is all from memory rooted in my former life doing software for the Superconducting Super Collider back in the 1980s.)