Out of your entire proposed itinerary, I only have any real concerns about one of the segments on the return, though the United website seems to think your entire outbound itinerary is risky.
Let's look at your flights in detail:
Departing Friday, October 14, you have the following flights:
UA 846 SCL-IAH 10:00 pm - 5:50 am +1
UA 404 IAH-SFO 7:10 am +1 - 9:35 am +1
UA 35 SFO-KIX 11:15 am +1 - 3:00 pm +2
The website marks each of these as a "Risky connection."
Taking a quick look at recent stats for UA 846, we can see that this flight is almost always 30-60 minutes early into IAH. You should actually have two hours or more to clear immigration and get to your next flight, and IAH is relatively quick to get through (especially when you're on the first plane to arrive in the morning). And if you're using the Visa Waiver Program and you have visited the US before (since 2008) then you can use the Automated Passport Control kiosks to speed your way through immigration.
All of the real risk from this itinerary comes from the possibility of missing the IAH-SFO flight, or from it being significantly delayed. But its historical records look pretty good, too. It's almost always on time. Once in the last 10 days it departed and arrived 30 minutes late.
I wouldn't consider this particularly risky, but if you do miss a connection, you will most likely end up leaving SFO at 7:20 pm on UA 875, connecting in Tokyo to NH 93 and arriving at 8:20 am +3.
The return itinerary you selected was:
UA 34 KIX-SFO 4:40 pm - 10:35 am
UA 721 SFO-IAH 2:30 pm - 8:25 pm
UA 847 IAH-SCL 9:20 pm - 8:50 am +1
I'm not sure why, out of the three options you had available, you selected this one. It's the one I would consider most risky, because of UA 721 SFO-IAH. Here, you have only 55 minutes to connect at IAH to an international flight. If this flight is delayed more than a few minutes, you are likely to miss your connection.
You have two other good options to choose from at the same price, each of which has an earlier SFO-IAH flight.
- UA 1081 leaves SFO at 1:58 pm and gives you 1 hour 27 minutes to connect in IAH and 3 hours 23 minutes to clear immigration and change planes in SFO.
- UA 285 leaves SFO at 12:45 pm and gives you a whopping 2 hours 40 minutes in IAH and 2 hours 10 minutes layover in SFO.
Either of these choices would be much better than the one you had selected. I'd probably go with the former, myself.