3-Way Worries: Is My Wiring Safe?
The usual blunder is looking at wire position rather than purpose.    Anytime you work with 3-ways, your first priority is identifying the two messenger wires going to the switch from the same cable.  

However when novices change 3-way switches, they usually look closely at the physical position of the terminals on the switch, duplicating this on the new switch.  The problem is manufacturers totally randomize which screws are in which positions.  So the swap ends up shuffling the wires on the switch - and creates cases where the switch won't work in some positions.  

The right way is to pause before removing the old switch, identify the messengers (typically on the brass screws of the old switch) and then mark them with colored tape, e.g. I like to use yellow for messengers (they can both be yellow since they are interchangeable.) Be sure to mark the wires the same on both ends of the wire.  

The good news is there are only three possibilities - one wire is the common and the other two are the messengers - and often the common goes into a different cable than the messengers, which are always together.

That wiring

Homeowners doing their own wiring can be a problem because they can often get quite "inventive".  Worst case, if you have to tear work out, they usually do give you enough wires to do it properly.  If not, "smart switches" can often save the day.   

You can exclude a California style wiring because it would involve /4 cable or (illegally) two /2 cables paired.  The Carter system (serving hot or neutral, lamp in the middle, lamp lights when one is hot and the other neutral) is something to watch out for, not least because it is a wiring loop, which is bad.  All wiring should be physically in a tree topology.