IMO he just wasn't as careful as he thought he was, though still light years above the average killer. He left a breadcrumb trail of traffic cam footage leading back to him, and then needlessly stopped at a restaurant.
If it were me, I would've spent like a year or two getting jacked and buy the lightest motorcycle I could find that could still go fast enough to not pose hazards on the interstate. I'd ride at night, preferably in early winter/late fall when the night is long, and preferably on a night where forecasted temperatures don't dip too low. Every time I spotted traffic lights ahead, I'd get off-road and go around them, lugging or carrying the motorcycle with me. If you can bench press 200 lbs then you ought to be good. Preferably wear some kind of padding on my feet (while dismounted) to avoid leaving shoeprints. Take no phone with me. Pack a basic utility kit like food, water, a map of the route, calculator, pen and notepad, etc. As much as I could reasonably take with me on a motorcycle without it blowing away or whatnot. I wouldn't stop anywhere unless I absolutely had to.
Ahead of entering, I'd hide the motorcycle somewhere and use taxis to get around, paying in cash (my wallet, and every bill and plastic card in my wallet, would be treated ahead of time to remove fingerprints the best I could). My fingerprints are in the system, and as for DNA I'm fairly confident that some relatives of mine have taken ancestry tests. While using any taxi, I'd place some kind of pad under my butt to avoid leaving my sweat in the cabin, and I'd avoid resting my back or head against any part of the car. Instead, I'd use my gloved hands to hold onto the front seat and keep my balance.
I'd be wearing gloves, a beanie cap, flu mask, thick clothes, and colored contacts. All this save for the flu mask and colored contacts would be purchased from a garage sale or whatnot ahead of time, preferably from two or more different ones, where I paid with cash, at least one month in advance. In the winter I wouldn't look out of place wearing this getup. My outward layer of clothing would be of some visibly different color when worn inside out. I'd bring both my real ID and a fake one; if stopped and questioned before the act, I'd use my real ID and give a prepared story for why I was in New York. Then I'd give up the attempt and go home. If stopped and questioned after the act, I would risk a fake ID and just hope I didn't get arrested.
In winter, I probably couldn't stay outdoors overnight. Preferably the act would be done on the same night that I arrived but if I was staying multiple days in NYC then I'd have rented an Airbnb with a burner phone (or using a burner app on my normal phone) and paid with cash. All in advance, of course. If I had to withdraw a lot of money from my bank account to prepare for this, then I'd do it incrementally as opposed to all at once. All travel in NYC would be done by taxi as opposed to on-foot, and traffic cams would be avoided simply by ducking the best I could while in the back seat. The exception would be the act itself, during which I'd have to do some walking outdoors. I'd schedule one of the taxi cabs that I rode in to meet me again at a certain time and place, and that's how I'd either make my getaway from the city or return to the Airbnb (if daytime and I needed to wait until it was night again).
Finally, I would return home the exact same way I came. Depending on how long I was gone, my absence would be noticed. I'd have taken time off of work, not exactly matching the time window of the act but a little longer than that to deflect suspicion, and afterward claim that I was playing video games at home for several days. I'd keep all the lights on in my home to consume electricity, and the curtains drawn, for the duration of my absence. All web searches that I did ahead of this would be done browsing in Incognito Mode, VPN, and the most private search engine that I knew of.
...If this sounds like a huge hassle, that's because it is. It's extremely hard to pull off a perfect murder in this day and age, and even what I just described isn't without its vulnerabilities and potential points of failure. My guess is, Luigi Mangione wasn't anywhere near as thorough as I've described above.
