Of course there are weak points in Descartes' philosophy. Every philosophy has its weak points... perfection has not been reach yet, and I am not sure it can be reached someday.
There is no doubt the scientific method in the "Discours de la méthode (1637)" is of critical interest regarding the modern sciences, however the whole philosophy from this "thinking being" (
) is far more than just this.
One of his weakest point, in my opinion, is to categorize everything. Most of the time his categories are exclusive or based on a single point analysis. The advantage is that you can solve problems separately and then add the solutions to reach a global solution. However this method makes the people who use it face the problem in a given manner that is not necessarily the best way to come over. In other words, there are cases in which the "Descartes method" hides the solution due to the way in which the method introduces the problem. Another analysis that would generally be more global and avoid exclusive categories or avoid any categorization at all would be of great help.
As I said each method has its imperfections, there is no best one, there is simply the most fit to the situation
Hope you'll understand what I meant