You also have to make sure that the shifter bell crank for the lower unit on the starboard side of the engine does not hit that breather hose on from the carb to the valve cover. That will keep the drive from going all the way into gear and will cause jumping out of gear. This is why Edelbrock/Weber carbs do not work well on an OMC Cobra application, the carb is too wide on the side this next to the shifter linkage. OMC engines came with the Quadrajet 4bbl until about '90 or so and then they switched to a Holley 4160 4bbl I believe. Ether one of these carbs fits the engine set up better than the Edelbrock/Merc/Weber carb.
I noticed a hold down screw for the distributor cap missing. I strongly recommend that you get this boat to a real marine mechanic to sort out these problems, to make it safe to operate. The engine itself will work fine, its the carb/linkages that need attention. Make sure the mechanic has OMC Cobra experience and will know how to make sure the shift linkage is set up right and the ESA system works. Otherwise this boat will either not shift right, & not come out of gear.