Reasonable people will disagree about about which challenge is the most important, but here are some serious candidates.
1) Comprehension: Much research relies on familiarity with relatively arcane details (theorems, estimators, institutions, solution techniques, algorithms) specific to a particular subject area, so that economists not intimately familiar with those details are required to accept the validity of the research more or less on faith.
2) Contradiction: In many areas, research results are contradictory. Knowing this makes consumers of research reluctant to accept results on faith. Understanding the sources of these contradictory results and resolving them is a substantial undertaking.
3) Replication: In empirical work, replication of results has been a major problem. Data may be confidential or proprietary, and many public data series are subject to revision. Limited sharing and interoperability of computer code is another stumbling block.
4) Professionalism: There are strong individual incentives to exaggerate the importance of results and minimize their limitations and appropriate caveats. In addition, many researchers set out determine to prove or find a particular result, ignoring all evidence to the contrary.