LA Clippers
1 Biggest problem: Kawhi Leonard may be cooked
Over the past few seasons, the LA Clippers' championship chances have continually been spoiled by a Kawhi Leonard injury. He hasn't seem to be able to remain healthy in each of the last few seasons and the early indications is that will continue to be the case this year. For the Clippers, that has to be considered their biggest problem. For the most part, this team was built around Kawhi as the team's No. 1 option. With Kawhi not being healthy, the argument could be made that it devalues this team completely.
Without Kawhi, the Clippers aren't a championship contender and may not even be a playoff team. Even though there's still hope that Kawhi will be able to return at some point this season, the fact that it's not a guarantee is a big issue. It completely brings into question whether or not the Clippers should move forward with this core. At this point, a rebuild may be necessary. If that's not clear already, there's some malpractice taking place in the front office.
Los Angeles Lakers
1 Biggest problem: They need another starting-caliber big man
After a pretty hot start to the season, things have certainly cooled off for the Los Angeles Lakers. They still have a pretty good offense but their defense continues to leave much to be desired. Above all, however, if the Lakers want to emerge this season as a championship contender in the Western Conference, I do believe that they'll need to add another starting-caliber big man at some point before the NBA Trade Deadline. If they want to preserve Anthony Davis for when it matters most, adding another big is the way to accomplish that.
Whether the Lakers are able to pull off a move for a starting-caliber big or not could end up dictating whether they'll be considered a feasible contender in the West or not. The West is wide open at the moment. Other than the Oklahoma City Thunder, there's little other certainty in the conference. If the Lakers want to throw their hat into the ring of contenders, there's a window for them to do so. But I do believe that making a difference-making in-season acquisition will go a long way in this team accomplishing that.