Online travel sites are very useful. I use them all the time as a crib sheet. If I am asked about an itinerary, I like to make sure I have not missed the glaringly obvious. However, in many instances, that is all online sites are good for - a crib sheet.
As an agent, I do filter out the options which may be cheap but still, represent some rather uncomfortable features. Not to mention, some of the more outlandish ways of getting from here to there.
Transfers through China, for example. These may look a very cost-effective option.... but what happens if you are delayed and have to spend a considerable amount of time waiting for a connection? You are stuck in a transit lounge as you do not have a visa to enter China.
Another option I try to avoid are "one horse wonder" airlines. These are airlines that are very limited in size. They may only have a couple of aircraft - so if there are any technical issues, you have no option but to wait until the aircraft is fixed.
Some other situations to avoid are where there is no "Plan B". By this, I mean looking at what happens if you miss a (valid) connection. Is there a later flight where you may be accommodated? Or do you have to wait until the next flight which is (in one example I had to deal with) two days later? You may - that's "may" - be found somewhere by your airline, depending on circumstances, but I suggest you only look at situations where there is a plan "B".
You should also be aware of airlines that are based in what may be troublesome areas. I am not going to mention any names, here, but the far end of the Mediterranean Sea has its issues, at present.
Watch the time of journey. Always change from "By Price" selection to a "Journey Time" selection. In this way, you can compare the fastest time and then evaluate any cheaper fares accordingly. You would how many people miss the "Long Wait - 20 Hours" .
Be careful where a low cost carrier is mixed with legacy airlines. Some low cost airlines do code-share (JetBlue, for example) in some but not all instances. If the trip involves a low cost airline meeting a legacy airline, (or vice versa) be aware of the small print. This may often say something along the lines of "This is a split ticket, please read the conditions" or similar. Do read the conditions very carefully as they are generally very wooly-worded. In many cases, the conditions should read: "If you miss the connection, your only option is to buy a new ticket at the prevailing rate and if applicable, for any onward connections as well!"
Reading through my social media streams, it is clear that many people are not heeding the (many) pitfalls of online booking. I do not deny that simple "Here to There" (in one flight only) type bookings may be easily accomplished online with little to worry about BUT anything more than that, you are still better off asking your travel agent.
May I wish you all a Happy and Prosperous New Year!