On the GOP side, Have Reagan pick someone more Conservative than Bush to be his running mate, alienating moderate Republicans and some of the what would be "Reagan Democrats" causing them to stay home or vote Anderson. A gaffe or two by Reagan or a lapse that makes him look senile would help to.
On the Democratic side, have Kennedy so well enough in the primaries for a brokered convention, but have Carter get the nomination in the end, causing the liberal Democrats to vote Anderson or stay home.
As for policy that's a little trickier. I'd expect a smaller increase in defense spending and no tax cut. With that said however, Anderson, if even a liberal one, was still a Republican so don't expect new entitlements either. Also, expect the Democrats to keep the Senate in 1980, as I doubt Anderson would do strong enough to flip it like Reagan did.
I think Reagan could probably hang on to a share of the "Reagan Democrats" for two reasons, one being Carter's inextricable linkage to the hard times of later '79 and 1980 (and related to that, the low tolerance for signs of male weakness in blue-collar manufacturing culture) and the fact those "Reagan Democrats" really bore a more polite name for "non-Southern George Wallace voters looking for a home," which they definitely had with Reagan.
But, I think you are entirely (and for Reagan, devastatingly) right that he could bleed liberal and moderate/Rockefeller Republican support like a stuck pig if he picks, say, Jack Kemp for the youth factor or similarly Thad Cochran to cut directly at Carter in the South, or another choice shown to be aligned with the right. Given the clumsiness of Dole's campaign, Bush had rapidly become both the Ford-surrogate in the race and despite his decades-long efforts to be a Texan
manqué was tied through his daddy to the last of the old Northeast Establishment. Barring what was arguably Reagan's best choice that year other than the whole business with Ford -- Howard Baker, the moderates' moderate and a shot right at the Georgia state line vs Carter's continued strength in the South and border states (most of which he lost by 3-5% or less, TN and AR were damn near recounts, even in what turned into an electoral college landslide), but who could not be chosen because he was "impure" on the Panama Canal -- Bush made the most sense for Reagan, Rumsfeld's lost telephone number or no. But I think going for, say, Kemp, and then having some slip ups especially
against Anderson -- maybe Reagan has a "1984 first debate" style flop but in that one-on-one with Anderson -- could really hurt him with the GOP "left".
On the Democratic side, if Hugh Carey had succeeded in his efforts to "unbind" the delegates for the Democratic National Convention and Teddy had been able to do considerably better picking off buyer's-remorse Carter votes, the "he wuz robbed" factor would go up a great deal through the Northeast and New England. It's not clear that would prevent simply another three-way race a la 1912 and 1992, where either one side gets what is effectively an unfair advantage because the other side in the usual two-party arrangement split its votes (as Wilson and Clinton did respectively) or whether it would really become a three-way race with Anderson winning enough states to force the whole thing into the House.
Anderson was indeed, despite his conservative beginnings in Congress, the last hurrah of the liberal Republicans, and to some degree he was by then on the full on "liberal" end of the party, out to the left of the more statist and hawkish Rockefeller Republicans. Fiscal rectitude would be the cornerstone of his administration, but also those efforts to make innovative changes. And, to answer
@GeographyDude from earlier, the "50/50 Plan" was 50 cents a gallon tax on gas -- itself a post-Keynesian maneuver trying to bring the demand curve back in line and also "squeeze out" excess inflationary monies from circulation and put them back to either stabilize the public fisc or be transferred to government-based investments to stimulate productivity and employment -- matched with a 50% reduction in payroll tax on Social Security. The latter might have posed some actual problems for the trust fund if carried on too long, but it was linked to the sincere and admirable desire on the part of the most liberal Republicans of that era (Jack Javits and Mark Hatfield made similar suggestions) that actually put them in tune with the more social-democratic end of Democratic policy like "McGovernomics," namely that the tax base of Social Security needed to be a lot more progressive, that the days of ensuring its existence by having workers just pay for themselves in payroll tax like a company pension was over-burdening especially when they weren't getting raises to match inflation, and that general liberty of citizens -- including real economic liberty, which these ultra-liberal GOPers still cared about -- meant prevention, as TR had warned at the dawn of the century, of concentrated wealth in too few hands. So it's possible Anderson would have worked with the Democrats to come up with a new revenue model for Social Security -- but that's as much of a classical entitlement program as you're going to get out of him. More likely, because there were strong ideological similarities despite their difference of party affiliation, you get something like Gary Hart's Targeted Investment Initiatives, specific grant or more often loan programs (USG gives you cash but you have to pay it back as it helps you improve your situation) to support sectors of the economy that could help offset the stall and decline in heavy manufacturing.
The other big thing for Anderson is if he can somehow manage a better VP. If it's about a revolt of the liberal Republicans he could do no better than war hero, ultra-liberal (but fiscally cautious) tower of integrity John Chaffee, even if Chaffee's from a small state (it's not like Patrick Lucey was that much of an Electoral College improvement, and Chaffee cut a much better public figure.) Or if he could somehow talk Hugh Carey, who Anderson tried to court and who was a decidedly liberal Democrat -- though into fiscal probity -- and friend of Teddy Kennedy to run on a sort of "national unity" ticket appealing to the great American middle -- the chance that would give Anderson, backed by a liberal Catholic New York governor, to take both Illinois and New York, would be a real game-changer, plus potential knock-on effects in New England, and traditional Progressive (in the old third-party sense) strongholds like Wisconsin (Lucey or no Lucey), Montana, and Oregon. Now all of a sudden you're talking about a presence that could really knock the EC into the House.
And yes, a stronger Anderson presence rather than straight-ticket Republican voting probably does preserve a Democratic majority in the Senate by a little ways. There were at least five Senate seats that were in very grave danger no matter what because they were in states that were trending strongly partisan towards straight-ticket GOP voting, and included some big targets: Gravel in Alaska (who, after all, was primaried IOTL even before the general), Church in Idaho, McGovern in South Dakota, Culver in Iowa, and Bayh in Indiana. But in this scenario the Dems can probably stop the bleeding at five or six seats rather than twelve (maybe six, Talmadge still narrowly lost in Georgia though Carter polled close to 60% so there was clearly some crossover between Georgian patriotism -- "our own president" -- and GOP-trending votes against Talmadge) and hold the Senate.
Now, does all that produce a President Anderson? It's still going to be bloody hard to get him through the House voting. But there is
just a chance, having made it that far, that Republican moderates see their chance to fight back against the New Right and that Democrats feel like they can live with Anderson and start over after the failed Carter experiment, particularly since there's a good shot that a special election will cause the Senate to confirm Vice President Mondale anyway. Despite the fact a more effective Anderson campaign probably
could pull 20-25% of the electorate, he may actually have a harder road to the White House than TR in 1912 or even Perot in '92.