About 18650 batteries possible accidents with reversed polarity
With just the voltmeter connected as shown, no, nothing should blow up.  This is assuming a typical voltmeter with 10 M&Omega; or so input resistance.

However, if you connect this battery string to a real load, then bad things could happen to BAT3.  Think of the limiting case where the load is a short circuit.  Now you have three batteries trying to charge one.  That's not going to end well.  Assuming all batteries start out well charged, BAT3 will be rapidly overcharged.  It could leak, blow up, catch fire, or the like.

This may not be good for the other three batteries either.  You basically have two cells driving the internal resistance of four cells.  That could result in excessive discharge current, which could also cause BAT1, BAT2, and BAT4 to exhibit "unfortunate" behavior.