The person with the best grasp of Quebec polling (in TC's view) is Université de Montréal sociologist Claire Durand. In a post on her blog Ah les sondages, she made several estimates of the potential outcome based on the polls. Her scenario #2 here (en français) was not all that far off the final result estimating the PQ at 32.5% [actual was 31.94%], the PLQ at 28.9% [31.21%] and the CAQ at 27.7% [27.06%].
The problem of underestimating the Liberal vote is not new and it showed up again in 2012. The reason Durand's scenario # 2 was closer than others was that she disproportionately distributed undecided voters to the Liberals, giving them half of that group. In a close three way race such as this one, an apparently small shift can make a significant difference. Durand discusses it further in her post-mortem.
The PQ now has a government and a leaderless Liberal opposition, so it will have some breathing room. However, it has one of the weakest mandates of any newly elected administration in Canadian history. The 1927 Manitoba election gave the Bracken Progressives 32.4% of the vote, although they won a majority of the seats. I have been looking but haven't yet found a weaker popular vote (the BC Socreds were a little lower in the 1952 BC election but it wasn't a first-past-post voting system).
The PQ faces an electorate opposed to its sovereignty plans and with little appetite for a referendum. The same CROP poll that reported 62% opposed to sovereignty found that 68% of Quebec's citizens are opposed to holding a referendum. For all the initial bluster of their post-election statements they will have no choice but to proceed cautiously.