Whatever is going on with that blue wire spliced into the yellow looks fishy. So does the free hanging solenoid connector that was replaced with the black wire.
It looks like the positive cable has been replaced at one time with a temporary battery clamp.
I know some aftermarket wiring diagrams will disagree with me, but I contend that the proper distribution point is never a battery clamp. It should be either like the old way most manufacturers did it, off the solenoid, or like modern cars off of a distribution block that connects with one heavy gauge wire to the battery clamp. Too much chance of shorting out or overloading otherwise. Likewise, grounds go to the block or frame.
Think of it this way: the battery is not the source of power, the Alternator is. The battery just helps the alternator when it's not keeping up, so you want the connection points to center around the alternator's connections which are the engine block and the solenoid or distribution block. The battery is just hanging off a side lead.
I don't trust the brush-on insulator and the twist connections. Automotive crimp connecters or soldering (there's a debate about soldering) and shrink tube are the way to go. Self-fusing tape works when you forget to put the tube on first, and doesn't leave a sticky residue or unravel. Vinyl electrical tape is not good around oil, gas, and engine heat.
Either someone was hiding a problem or wired in an accessory wrong, but the blue and yellow wire need to go and I'm not thrilled about the looks of that battery cable.