What are the basic difficulties of using the collocation techniques for solving PDE’s?

Here are a few more that come to mind (some related to those you have mentioned). Difficult to prove convergence of collocation methods in general and to bound the associated errors. The weak/variational form for FEM enables one to bound the error and to ensure convergence to the exact solution (esp. for linear problems ) that is one-sided with refinement (more basis functions via h-refinement or higher-order elements/approximation). In finite-differences too such statements on the errors can not be made (errors can be positive or negative). Collocation schemes using radial basis functions (RBFs) are well-known and they are amenable to mathematical (convergence) analysis (global RBFs). Even here only for a select few global bases (e.g., multiquadrics or Gaussian) is the stiffness matrix invertible (strictly positive-definite) and hence the data approximation problem (i.e., essential boundary conditions to solve a PDE) is solvable. The stiffness matrix becomes fully populated (unlike weak formulations using compactly-supported basis functions as in FEM) in collocation schemes and handling natural BCs also requires extra work and care (unlike weak formulations). A big plus of these is that spectral convergence is obtained (global bases), and hence fewer nodes/unknowns suffice to get very good accuracy. The trade-off when one attempts to use compactly-supported RBFs is that K is no longer strictly positive definite and spectral convergence is lost. Here's a recent paper that talks about RBFs and the Gibbs phenomena.