The phrase "a weakness of the current" is correct and usable in written English.
It can be used when discussing a flaw or limitation in a current situation, system, or process.
Example: "One significant concern we need to address is a weakness of the current strategy that could hinder our progress."
Alternatives: "a flaw in the current" or "a limitation of the current".
It is indeed a weakness of the current state of knowledge that individual quantitative-trait loci have not yet shown up.
That there were only two WM task difficulty levels, one rather easy and one rather difficult may be considered a weakness of the current experimental design that was not designed with regression analysis in mind.
A weakness of the current study is its cross-sectional nature.
The lack of such development is a weakness of the current study.
A weakness of the current study is that we calculated adjusted SMA-derived arm elevation angles using the same algorithms for all subjects.
A weakness of the current study is that we provide little in the way of mechanistic insight for the increased TLR activity.
A weakness of the hospital's current system is the inability to capture deaths outside the hospital in the communities served and, thus, a lack of information on perinatal deaths occurring at home.
It follows that a weakness of the model framework, in its current form, is the difficulty in confronting the model with quantitative data other than in regards to its qualitative predictions.
A further weakness of the current approach is that it relies on a good separation of the two clusters corresponding to the ON and OFF pathways.
A central weakness of the current Regents testing regime is that the exams are typically scored in the schools where they are given, sometimes by teachers who grade their own students.
A second weakness of the current study is that we did not assess the reliability of arm elevation measures derived from the SMA.
