With DIP type components, a sub-par fluxing method (foaming a no-clean), and a chip wave where one is not needed are formulas for bridging and insufficient wetting. If you have SMD's on the wave solder side of the board greater than 0603, and no SOT23's, and all SMD's in the "correct" orientation whereby both pads and terminations are hitting the wave at the same time, hence no shadowing of your SMT devices, you may be able to do without a chip wave. Sometimes the chipwave CREATES shorts because your flux activator has already been burned off at the chip wave and there is a minimal amount left to obtain ideal wetting conditions, as well as "cleanup" and peelback from the main wave. Personally, I've had poor results at the wave, with a similar situation like yours with the older Kester (circa 1990) formulations. Hence, another solution, if you absolutely must use a chip wave, would be a flux change - try to use a newer chemistry with better activators, like Carboxylic acid, and fluxes with more surfactants content. If your budget permits, switch to spray fluxing as well to get a better and more controlled flux deposition and eliminate the need for titration and specific gravity checks.
Other things worth trying to mitigate solder bridging - slow down the conveyor speed a bit to reduce contact length. These variables are directly proportional, but at the same time, reduce your pump speed to get the same dwell time. If possible, measure the dwell at both Chip and Lambda waves if you have a profiling device. General paramaters which yield good results - about 0.5 s at the Chip wave and 1.5 - 2 seconds at the main wave. Wave Soldering is an artform, my friend, and knowledge of the Physics and Chemistry behind the process and all the variable interactions will help you a long way. Best of luck....
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