Exploring Classical Mechanics by Kotkin and Serbo (Oxford University Press) is a collection of 350 fairly advanced problems, with solutions. It deals with classic material, such as fixed point analysis, small oscillations, scattering and includes problems in Lagrangian and Hamiltonian mechanics.

An alternative is

Classical Mechanics Illustrated by Modern Physics by David Guéry-Odelin and Thierry Lahaye (Imperial College Press) which contains longer problems than Kotkin, but is not as expansive.