The best replacement for problem is issue.

The best alternatives to problem are rated as following:
★★★★★  issue
★★★  opportunity
★★★  incident
★★  symptom
★★  inconvenience
★  dilemma
★  solution
★  anxiety
★  challenge
★  predicament
★  invalid mmi code
★  alcoholism
★  yg
★  any problems
  part of the solution
  diagnosis
  conflict
  purpose
  trouble
  problem statement
  hustla
  question
  research question
  issues
  progress
  hustle
  emotion focused
  situation
  little problem
  an issue
  alcoholic
  hypothesis
  panic attack
  problematic
  condition
  cassidy the hustle
  transmission problem
  incident management
  nursing diagnosis
  thank you

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Speaking about problem, one probably shouldn't forget about solution.

Other search terms related to problem and their ratings are:
★★★★★ solution
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Google Trends

Scale is based on the average worldwide traffic of problem in all years. Click on graph for more.
problem
issue
opportunity