There's usually enough play in the screws slots to align at least the bottom part of the frog to the mouth. If that doesn't help grinding is the only way, it's just a question off what exactly to grind - back of the frog that goes into the saddle, the saddle on the body or the front of the frog. The latter is the most work I think.
does the blade fit right now? If you mount the blade with the frog as-is, is the blade skewed? Along the lines of Jack’s suggestion, you might put the frog in semi-tight, mount the blade, twist the frog until the blade edge is square to the sides, then dismount the blade and tighten the frog screws.
Once the blade is cutting correctly, that’s the best you can do with that frog, no matter what it looks like.
This suggests that the mouth is skew rather than the frog. If so, just fine the mouth ... if you wish.
A close set cap iron provides tear-out mitigation rendering the role of the mouth irrelevant, does it not? So long as shavings are cleared do we need to care what the mouth opening looks like?
I was never convinced a "tight mouth" was a practical way to control tear-out?
Bill, an open mouth is not an issue. Anyway, this is necessary to use a closed down chipbreaker. On the other hand, a mouth where the blade may be set evenly is helpful in adjusting projection.
2. The back of the frog that goes into the saddle is not milled straight.
3. The face of the frog is not milled straight.
4. Screw slots are not milled parallel to frog's sides.
Number (1) is probably the trickiest to check, unless you have diemaker's square, but you could figure that by exclusion. The question is how to fix it? A mouth could be opened a little as Derek has suggested, even if it's skewed, might be beneficial even, but other than that it would probably require a mill.
Buy a replacement frog. They're all over EBay for all brands and vintages.
You can obviously check mouth square to the sides with any decent square.
Put a square on the frog (take it out) and see if the tips of the frog are square to the body. If they're not, or out of alignment with each other (one longer than the other), just use a mill file straight across until they're square and even in length.
You can also register a square over the wings of the plane and sight down over its edge to see if the bosses look way out.
If you have "several" like this then I would be suspicious about how you're setting them up. The odds of acquiring a lot of planes with the same kind of defect (especially this one) must be vanishingly small to the point of impossibility, even for mass-produced Stanleys.
So after some extensive measuring, I have resolved the issues on both planes.
The first was fairly simple. Turned out to be a bulge down low on the body casting that was interfering with the frog. Took a bit off and it was fine.
The other plane was a total mystery. Upon inspection, everything looked fine. The previous owner had re-flattened everything and it looked like he did a fairly decent job.
I finally decided to set it up and measure it on a CMM and things became more clear. It turns out, the problem as actually the accumulation of multiple different deficits in different parts of the frog that by themselves wouldn't have been a big deal. All combined, it was a perfect storm of everything being just barely off.
The saddle was slightly rounded, but also barely angled to the back and one side. The back of the frog was also minutely canted, but in the opposite direction of the saddle.
The "feet" of the frog were not quite co-planar and were not quite parallel to the back mounting surface of the frog. Only the very front surface of them touch the body, and on one of them, only one corner of the front edge actually touched.
The end result of all these mismatches is that when you put the frog in place by hand, it felt quite securet. When you screw it in place with some pressure, the frog rocks and twists on the saddle just a bit. One of the frog feet lifts and loses contact with the base and I think the other actual deflects a tiny bit at the tip - the only contact area.
All of this put together makes for an overall twist that causes shavings to jam on one side.
I suppose I should have taken some pictures, but it didn't cross my mind until later. A buddy of mine is facing all 4 surfaces true on his mill - mostly as in experiment in restoration. It should work great once he is done. I don't know if a frog that is lower then usual will cause trouble with the chip breaker being extended too far, but we will find out.
This has been a good learning experience, I have run into all of the issues in the past, but they are usually easier to detect. Having them all be just barely off, but interact in the worst way possible was kind of an eye opener.
The previous owner had re-flattened everything and it looked like he did a fairly decent job.
Well there you go. I am always amazed when I see people who are unsure about their woodworking ability confidently attack the machined shortcomings in their planes with hand files and sandpaper. I'm glad it wasn't enhanced beyond repair.
Ole boy goes into the shop, tries to four-square and thickness plane a 3' long by 8" or so wide board, says "screw this," and starts his adventure in plane fettling.