Is there any way to view the completion percentage of the game?

According to the Official Guide, the completion rate is shown on the lower-left corner on the Sheikah Slate's map, and adds up by .08% for every "relevant objective", which could be tasks such as;

• Finding 1 of the 900 Korok seeds
• Completing 1 of the 100 shrines
• Defeating one of the bosses
• Discovering a new location

Hope this helped!

Once you have defeated Ganon and thus completed the main quest for the game, your saved games will be indicated with a star to show that you have completed the game. This will also reveal the % completion on your world map.

Things like treasure chests and adding things to the compendium does not count towards this %. As already mentioned, only specific things counts, and they all weight in the same, which is slightly more than 0.08% (no, it's not 0.08% and neither is it 0.09%, it is some unknown number, but approximately 0.081%, which is why it sometimes seems to add 0.09%).

It should also be mentioned that completing shrines yields you 0%. Finding the shrine and activating it, however, yields progress towards completion. I find that wierd, but that is how it works.