I've owned this boat for 8 years.  It's been only in the garage, oil changes regular, winterizing, etc.  2 other owners before me according to the last seller.  1050 hrs.  It's been a center point for my kids thru their teens and so much for for us.    This is background on the general condition of the boat.

Anyway, over the past month the boat has had some trouble starting up.  I have an on-going electrical issue with starting which I won't go into (yet) but this is a crank-crank-crank but no catch until finally it just catches and will run but we have to keep some extra throttle on at first.  Once we've warmed up it would do ok.  

Within the last 3 weeks it started to run rough also while we were towing skiers, etc., mostly on the very low end and would sometimes stall while idling.  Once underway (higher throttle) it would basically behave.

Trouble starting but then running ok at higher rpms sounded like it could be a fuel issue.  It's been 3 years since I replaced the fuel filter so I made that replacement and I also cleaned the stator and tips on the distributor (last night) -- they weren't all that dirty.  This morning at the lake it practically jumped into action as though all our miseries were behind us.  As I celebrated during with our early am glass runs today, the rough running returned (about 60 minutes into the trip).  Before we pulled off the lake, the boat had stalled twice on us again.  So whatever good I did swapping out the fuel filter and clearing the tips had no permanent effect.  

Other things I've thought of:

>>Spark plugs and wires were changed in 2019.  Haven't checked plugs again yet

>>Fuel bad?  Should not be -- running high octane non-ethanol unleaded fuel with no stabilizers or lead additives

>>Fuel pump?  Maybe.  I haven't checked the pressure but just replaced the sight tube and nothing obviously amiss plus it runs ok at higher rpm

>>Carburetor?  I've done nothing with this since I purchased the boat except 1 dose of Sea Foam in 2019

I tried reading thru the engine service manual -- some good ideas in there but many require special tools.

Other (concurrent) problems:

>>Boat occasionally will not turn over at all mid-trip (when it's hot).  Sometimes replacing the solenoid makes a difference.  This seems to be an electrical issue because the battery remains pretty strong

>>Slow oil leak from valve cover gaskets but we keep it topped up -- maybe because the engine expects leaded gas and we have been doing only unladed

Thanks for any insights.  

You mention that you cleaned the rotor and cap terminals, but if you have points that need some cleaning, adjusting or replacement) that would be a good place to start.

Or get a tuneup kit with cap, rotor, points and condenser..............or get an electronic conversion kitand a new cap and rotor.

Next I'd probably be thinking about taking the carburetor apart for a cleaning/rebuild.

Oil leaking from the valve cover gaskets...........you could tighten the bolts a little or you could preferably replace the gaskets. They're old and tired of doing their job 

Tightening too much on the bolts can warp the valve covers

If I pop the two screws on the distributor cap, I see 8 spots in the cap ("terminals"?) and a rotating arm on the bottom with a spring contact connection to the top.  Is this points or could it still be an electronic module?

If you have a point set in your distributor, it will look something like this:

If it has the EI then it will look something like this:

Post a picture of the distributor with the cap off and we'll tell you more.

It sounds like you haven't touched the carburetor since you've had the boat so if a general ignition tuneup doesn't straighten you out, it's time for some carburetor luv  It can get gummed up,crudded up with junk etc even with a filter in the system

Right now, only you know if it's got points or an electronic module. If it's got points and you don't know what they are, they probably need some luv too.

You can get a whole points tuneup kit with points, condenser, cap and rotor or just a cap and rotor depending on what you have.

Putting them back on is harder, because of that same pesky lower center bolt on the valve cover.

Pulling the manifolds can present a whole different set of problems if the mounting bolts are in bad shape or rusted in place

As far as taking the carburetor apart, a rebuild kit with all the appropriate gaskets and replacement pieces is good to have on hand before you get started.

There's a list number on your carburetor that will help to get the right kit.

Here's a picture of where to find the list number (on the front of the choke horn)

You could start with the ignition system and move on to the carburetor if necessary