If a paper is rejected by many journals before finally being published, will that cause conflict with the reviewers who rejected the manuscript? I had a manuscript written 3 years before. The results of the manuscript was obtained accidentally while doing some easy trial methods. Although the results were very interesting, but the method was very very simple. So I thought to publish it in a low impact journal to increase my number of publications. But things went very opposite and got rejected in 5 journals. Everyone were commenting that the method is very simple and may introduce the unknown errors to the estimations or computations. 

As no one was commenting other than the methods, so I had no way to modify anything. Very bad thing is that none of the journal took less than 4-6 months to take the first decision and my manuscript remained unaccepted for two years and half. 

Finally I thought to submit it to a high impact journal. Very surprisingly, the reviewers appreciated the simple method used and accepted the manuscript with a major revision to highlight few other things. 

My accepted manuscript highlights the same methodology which was rejected by 5 other journals. 

Will there be any conflict or issues when those reviewers (who rejected my manuscript) see my accepted paper after final publication?
Your referees at specialist journals said, basically, "These methods aren't good enough to answer these questions, because X." But the generalist high-impact journal may have looked more at the results than the methods.

If X is "we just don't think this is very sophisticated, and the tools are out of fashion," I suspect nothing will happen.

If X is "there are uncontrolled errors larger than your effect," and you haven't explained in your paper why that isn't true, someone might write a comment on your paper. This comment will look a lot like your earlier referee reports. The field will then decide who is right. (See, e.g. the "arsenic life" experiment for a recent high-profile example.)

Beyond this, if I saw the second case from a paper I refereed, and there was no attempt from the authors to address the points I raised, I would not be happy with the authors, and might be less likely to extend them the benefit of the doubt in future referee reports.