You can do this by having your app's main form implement the IMessageFilter interface.  You can screen the Window messages it gets and look for clicks.  For example:
  public partial class Form1 : Form, IMessageFilter {
    public Form1() {
      InitializeComponent();
      Application.AddMessageFilter(this);
      this.FormClosed += (o, e) => Application.RemoveMessageFilter(this);
    }
    public bool PreFilterMessage(ref Message m) {
      if (m.Msg == 0x201 || m.Msg == 0x203) {  // Trap left click + double-click
        string name = "Unknown";
        Control ctl = Control.FromHandle(m.HWnd);
        if (ctl != null) name = ctl.Name;
        Point pos = new Point(m.LParam.ToInt32());
        Console.WriteLine("Click {0} at {1}", name, pos);
      }
      return false;
    }
  }
Note that this logs all clicks in any window of your app.