With a long history dating back to the beginning of the 1970s, the Parks-McClellan algorithm is probably the most well-known alternative for designing finite impulse response filters. Despite being a standard routine in many signal processing packages, it is possible to find practical design specifications where existing codes fail to work. Our goal is twofold: (1) examine and present solutions for the practical difficulties related to weighted minimax polynomial approximation problems on multi-interval domains (i.e., the general setting under which the Parks-McClellan algorithm operates), and (2) using them, describe a robust implementation which outperforms existing alternatives.