Great comments from P_T and GoForthFast.
As an alternative to liquid electrical tape, you can also use adhesive-lined heat shrink. The adhesive lining melts as you heat the piece of heat shrink tubing and seals the splice against moisture. You can get an assortment from places such as McMaster-Carr. Look carefully at the temperature and chemical resistance ratings.
Adhesive-lined heat shrink is my wrap of choice; these days, I only reach for electrical tape as a last resort. Those strips of black tape holding up the wire harness will fall off in no time.
sjbmw328i - It looks like you are missing the center splash panel and some other plastic bits under the front end. You might want to consider installing them, even if you do have an aftermarket front bumper cover. In addition to providing a proper mounting location for the OE ambient temperature sensor and heated washer nozzle temperature switch (if installed), they help protect the bottom of the engine against dust, water splashes, and small road debris.