I'd swap the regulator, preferrably for a solid-state one. The mechanical-contact regulators are prone to getting dirty points, and having other problems. Normal voltage against a fully-charged battery will be somewhere in the high 14's, maybe 14.7 or so. Current flow into the battery at full charge will be about 10 amps or slightly more. The capacitor has only one function, filtering out noise in an AM radio. The system will work just as well without it.
Jerry