In analyzing what's exactly wrong with the Lakers, it's actually difficult to pinpoint what their main issue is.
Some nights they defend poorly in the half court. Other nights they can't hit their free throws. In another game it's turnovers and transition defense that does them in. You simply don't start as poorly as the Lakers have unless there are multiple issues plaguing the team.
A popular critique amongst fans is that the Princeton offense is the main problem for the Lakers. The argument is that the scheme doesn't fit the personnel or that it's too complex for this group of players to run effectively. And while I'd point to other problems as being bigger than the Lakers' adaptation of the Princeton system, there's some truth to the arguments that the offense hasn't yet clicked in a way that's allowing the Lakers to be as successful as they can be.
In exploring the major issues the Lakers are having in executing their offense, the first thing one notices is the turnovers. The Princeton offense is a read-and-react system and when all the players on the floor aren't reading a play the same way, the miscommunication results in miscues.
Here you see the Lakers trying to run one of their standard actions in a Princeton set. The ball is entered to Dwight Howard at the elbow by Steve Blake. After entering the ball he goes to the wing to set a screen for Kobe who pops out to get the ball from Howard. From there, Kobe attempts to use a screen from Howard but the set is already starting to break down.
Howard doesn't get a good screen on Kobe's man and, just as troublesome, Steve Blake hasn't yet cleared to the wing and his man has dug down to make a pass to Howard difficult. Kobe then tries to drive to the middle of the floor and then hit an open Blake on the wing but because the initial screen wasn't effective his man is in a good position to disrupt the pass and force a steal. The result is an easy dunk going the other way.
Another issue with the Lakers new offense is that it's still prone to too many breakdowns that force a devolution of the sets. This will often lead to Kobe being forced to bail the offense out in a way that is all too reminiscent of the 2011-12 season when the Lakers struggled on offense:
Here you see Kobe with the ball near the right shoulder of the arc on the weak side of the floor with Pau Gasol. This play has gotten to this point after the ball was reversed, giving Kobe and Pau the opportunity to run a two-man game against a defense that is spread thin.
However, the play is already breaking down. Rather than Pau being at the pinch post and Kobe having the chance to hit him with a pass, Pau instead comes out to set a screen. But he comes to the middle of the floor where all the help is. Kobe then goes away from the pick, but Gasol stays in the picture still looking to try and aid him in getting open. The result is over-dribbling to the point where Kobe ends up straddling the three-point line and head faking his man until he puts up a desperation jumper.
The fact that the shot went in is irrelevant. The bigger issue was the initial breakdown in the offensive set and the miscommunication between Pau and Kobe that led to the forced shot in the first place.
The Princeton offense is supposed to put players in positions where they don't need to over-dribble and can get good looks from the floor simply through to the motions of the offense. The sets are supposed to combine ball and player movement in a way that promotes offensive spacing and creases in the defense that can be exposed through further motioning.
However, what we're seeing with this Lakers team is that they're not yet able to consistently put it all together and produce the type of free-flowing offense that is the hallmark of this approach. More often than they'd like to have happen, the sets are disintegrating and leading to empty possessions.
Over time these things that should improve. The Lakers are smart enough as a team to get on the same page, make the right reads and execute their sets cleanly. So far, however, it just hasn't happened consistently.
So even if the Princeton system isn't the Lakers' biggest problem, it is certainly one of them. And until the Lakers start winning games consistently, issues like the ones above are going to be pointed out.