Year after year, the NHL playoffs are rife with upsets. This year, the eighth ranked LA Kings easily defeated the first place Vancouver Canucks. Top seeds defeat last place seeds less than 75% of the time. In general, regular season success is not a great predictor of playoff success -- lower seed teams won half the first round series in 2012. The upshot of this is that so long as a team manages to qualify for the playoffs there is not a lot of motivation to win first place or gain a higher seed. As a result, regular season games risk becoming trivialized in the eyes of the fan.
However, while relative point total isn't a great predictor of playoff success, head to head competition records can be. The team that wins the regular season series between two teams wins the playoff series between them 77% of the time. So, teams are likely to be more interested in playing a team against which they have a good track record than in playing the one that has the fewest points.
So, one way the NHL might ensure that the regular season remains highly relevant to teams and fans would be to reward top finishing teams by allowing them to choose their opponent. Rather than obligating a first place team to face an eighth place team that has their number or that is on a roll because an injured star rejoined just as the season was ending, give the first place team the option to choose any opponent from the 5th-8th place finishers. (The second place team would choose from the remaining three, etc.) This would allow the top finisher to pick the team against which they're more likely to have success and gives a much stronger incentive to keep fighting for a high seed late long after a team has qualified for the playoffs. This would provide much more incentive for teams to finish in first place and would keep fans interested long after their favourite team has qualified for the playoffs. Of course, a team has little motivation to fight for 5th rather than 8th, but as a matter of fact the lower seed teams are usually close enough to missing the playoffs that they require little further motivation other than securing a playoff spot.
(Another obvious way to make the regular season more relevant would be to introduce a bye system as is used in the NFL. Allow only 6 teams from each conference to make the playoffs and give a first round bye to the top two finishers. But this won't fly because owners are too fond of the money that playoff games bring in. They're not going to sacrifice four seven games series. Furthermore, there's a legitimate concern that a team waiting out a seven game series might not be as well prepared for the second round.)