The first ten minutes on an inherited deck are worth more than the next two hours, and the rule for them is to change nothing. Read it before you touch it.
What should you check before changing anything?
Three global properties tell you most of what you need: the number of slide masters in the file, the number of distinct fonts in use, and the canvas ratio the content was built for. A file with three masters and seven fonts is a merged file, and merged files behave in ways that look like bugs until you know what they're. A file whose pictures were sized for a 4:3 canvas and pasted onto a 16:9 one carries a specific, visible distortion that no amount of nudging will fix.
Then read the Slide Sorter for shape and the Outline for argument, just as you would on your own deck. You now know where the deck is dense, whether it has sections, what share of its titles the Outline can see, and how many of those titles are claims.
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Which repairs come first, and which should you avoid?
Only then start fixing, and rank the repairs before you begin. The useful ranking is slides fixed per minute, because it separates a change that propagates from a change that doesn't. Re-pointing seven fonts to two theme fonts touches every slide in the file and costs about fourteen minutes, which is over three slides a minute. Retyping fifteen stray titles into their placeholders touches fifteen slides and costs about twenty minutes, which is three quarters of a slide a minute. Both are worth doing when you own the deck. Only the first is worth doing when you have forty minutes before a meeting.
Two repairs are almost always wrong under time pressure. Restyling the master is the first, because a change to type, placeholders or the background propagates to every slide including the ones you haven't looked at, and you'll discover the side effects during the meeting. Merging duplicate masters is the one exception worth knowing, and only where their layouts already match, because that merge changes which master a slide points at rather than what the master says. Even then you check the result in Slide Sorter before committing, and you leave the masters alone on a deck you're handing back to its owners. Retyping numbers is the second. If a figure looks wrong, note it and ask; a deck you inherited is a deck whose numbers you can't yet defend, and correcting one without saying so is how a wrong number becomes your wrong number.
How do you move 4:3 content onto a 16:9 slide?
The 4:3 problem deserves its own arithmetic, because both available fixes are bad and you'll want to choose the bad one on purpose. A legacy 4:3 canvas is 10.0 by 7.5 inches; the widescreen canvas is 13.333 by 7.5. The 4:3 area is 0.75 of the 16:9 area. Fit the old content by height and it keeps its proportions, occupies 10.0 inches of a 13.333-inch canvas, and leaves 3.3333 inches of dead canvas, which is 25.00% of the width. Fill the width instead and everything stretches horizontally by a factor of 1.3333: a 2.00-inch logo becomes 2.6667 inches wide at unchanged height, and a circle becomes an ellipse 33.33% wider than it's tall.
Height-fitting is the right default. Dead canvas is a design problem you can solve. A stretched logo is a legal and credibility problem you can't, because somebody's brand mark is now the wrong shape in a document with your name on it.