I am planning to book LAX-HEL, MOW-LAX and going to travel from HEL-St. Petersburg and then onto Moscow by land.

Will I encounter any issues with boarding at LAX since I don't have a flight out of Finland?

Not because of that, but make sure to have paper evidence of the MOW-LAX flight and your visa for Russia ready when you board, when you arrive in Finland (although Finland may not ask), and at the Russian border.

Different part of the world, but I've often done open-jaw Asia tickets, e.g. into MNL and out of BKK a month later. Airlines have gotten really bad about wanting to see evidence of onward flights if you gap between flights exceeds a standard tourist visa stay for the country. For example, the Philippines grants only 21 days (though an extension to 59 is not hard), so a return out of BKK more than 21 days afterward is still not enough...they'd want to see an LCC or other flight leaving the Philippines before the 21 days.

And Thailand, at 30 days, really has everyone on edge because of various crackdowns and the back-to-back bit, making airlines concerned because pax in theory could be refused entry and the airline would have to take them back out.

This is quite a change from the late 90s when I'd book into and out of someplace like BKK on a 3-month trip and would arrange all the intra-region flights out of BKK.