At such a late time, it is not likely that Mondale would run for President, remember he had declined to enter the Democratic Primaries. To enter after April 1980 would be a distinct disadvantage in seeking the nomination.
The following would have already occurred before he drops out:
January 21: Iowa caucuses (both parties)
January 22: Hawaii Republican caucuses
February 1: Maine Republican caucuses (through March 15)
February 2: Arkansas Republican caucuses
February 4: Wyoming Republican caucuses (through March 5)
February 10: Maine Democratic caucuses
February 26: Minnesota caucuses (both parties),
New Hampshire primary
March: Virginia Republican caucuses (through April)
March 4:
Massachusetts primary, Vermont primary (beauty contest--no delegates at stake)
March 8:
South Carolina Republican primary (party-run)
March 11:
Alabama primary, Alaska Democratic caucuses,
Florida primary,
Georgia primary, Hawaii Democratic caucuses, Oklahoma Democratic caucuses, Washington caucuses (both parties)
March 12: Delaware Democratic caucuses
March 15: Mississippi Democratic caucuses, South Carolina Democratic caucuses, Wyoming Democratic caucuses
March 18:
Illinois primary
March 21: North Dakota Republican caucuses
March 22: Virginia Democratic caucuses
March 25:
Connecticut primary,
New York primary
April 1:
Kansas primary,
Wisconsin primary
April 5:
Louisiana primary, Missouri Republican caucuses (through April 12)
April 7: Oklahoma Republican caucuses
April 12: Arizona Democratic caucuses
April 13: Arizona Republican committee meeting (& caucuses)
April 17: Idaho Democratic caucuses
April 19: Alaska Republican convention (through April 20), North Dakota Democratic caucuses
April 22: Missouri Democratic caucuses,
Pennsylvania primary, Vermont caucuses (both parties)
April 26: Michigan Democratic caucuses
April 30: Delaware Republican committee meeting (& caucuses)
Cliff Finch had dropped out in early April 1980 after the Kansas and Wisconsin primaries.
Jerry Brown had also dropped out after the Wisconsin Primary.
This means the only person still running in the Democrat Primaries is Ted Kennedy if Carter Drops out at the end of April.
OTL Ted sweeps the June Primaries, so without Carter in he'll sweep the May ones too. This will I believe give him just enough to win the nominations, even if Carter's now released delegates choose someone else.
Barring another prominent Southern Democrat, I believe Ted would choose Jerry Brown for an east-west coalition. While in theory a good pairing, it will not adversely affect CA it will still go to Reagan in the election.
The following states would flip though almost 100% chance:
Massachusetts, 0.15% goes Democrat (+14 D)
Tennessee, 0.29% goes Democrat (+10 D)
Arkansas, 0.61% goes Democrat (+6 D)
Alabama, 1.30% goes Democrat (+9 D)
Mississippi, 1.32% goes Democrat (+7 D)
Kentucky, 1.46% goes Democrat (+9 D)
South Carolina, 1.53% goes Democrat (+8 D)
North Carolina, 2.12% goes Democrat (+13 D)
Delaware, 2.33% goes Democrat (+3 D)
New York, 2.67% goes Democrat (+41 D)
Maine, 3.36% goes Democrat (+4 D)
The above along with what Carter won which Kennedy will also carry would give Kennedy/Brown 173 Electoral Votes which isn't enough to win.
The following states have approximately a 50/50 chance of flipping. Kennedy/Brown would have to win most of these to actually win in addition to the above.
Louisiana, 5.45% (+10 D)
Vermont, 5.96% (+3 D)
Michigan, 6.49% (+21 D)
Missouri, 6.81% (+12 D)
Pennsylvania, 7.11% (+27 D)
Illinois, 7.93% (+26 D)
Connecticut, 9.64% (+8 D)
Oregon, 9.66% (+6 D)
If they win all of these 50/50 states then they get 286 Electoral Votes and win the election. (They can lose up to 16 Electoral votes worth of the above states and still win the election)
The Chappaquiddick incident can certainly hurt the Kennedy/Brown ticket, however Reagan was not one much for personal attacks in his campaigns. As such it might never become a major campaign issue. Indeed Reagan might even make it a point that we should not hold the incident against Kennedy, perhaps due to youthful error.
So if Kennedy/Brown wins all the above they have 286 Electoral Votes, and Reagan/Bush has 252 Electoral Votes. It would be a very close election. That's a best case scenario for the Democrats in 1980. If they lose PA, MI or IL though then Reagan/Bush has a win, and I'm not entirely sure Kennedy/Brown could flip all three states. (Edit Oops should of been IL not CT

)
Either way its going to be a very close race, much closer than Reagan/Bush vs. Carter/Mondale.
The effect on Congress will be noticeable too. The Democrats will lose less seats in the House. In fact I think overall you'd see maybe only 5 Democrats lose seats, as opposed to the OTL where 34 lost their seats. I believe i the Senate only 6 seats will change hands which leaves the Democrats in control of the Senate barely (52 seats, even after Ted losses his because a D will be appointed to it).
PS the % listed next to the state is the margin by which they were won in the OTL.