Hold it under a bright light and tilt and turn it to make sure you have gotten all the bent pins or haven't created other ones in your effort to straighten the ones you started with. If they are a tiny bit off sometimes you can still get it to seat in the socket with gentle pressure. Then when you throw the lock lever it will finish the straightening. The thing you want not to do is to force the chip onto the socket and fold bent pins completely over to the socket base.
I can add that if you view it from different angles while having a light in the background, you'll often see a bent pin appear shiny (Reflecting the light) while the others do not at a given angle or view - That's an indicator of a particular pin being bent. Also know while setting it into the socket and locking it in will straighten the pins, it only does that to an extent, sometimes a CPU will simply be a touch stubborn to get in after pin(s) have been bent period. As mentioned, NEVER force one into the socket use only a light amount of pressure. If it's not wanting to go, take the CPU and repeat the process of finding bent pins and always be sure you have it oriented correctly to the socket as in the gold arrow on the CPU lines up with the board's socket arrow - I've been guilty of thinking it was right but it wasn't before.
I use a miniature flathead screwdriver for this most of the time, esp if a pin is really close to or even touching another pin. I use it to get them separated then work the pin as needed.
The method of looking straight down the rows is good and I look at them in straight and diagonal views since a pin can bend in any direction it wants. Another thing is sometimes even after a pin has been straightened, it will still appear bent due to a curvature or sway it might have due to it bending and you can't get rid of it but that's no problem - The trick in that case is to
get the tip of the pin where it should be, then install the CPU and the socket will help take some of the sway or curvature out. The biggest thing in any case is to get the tip of the pin where it should be so when you apply pressure, the pin will begin going into it's hole. Just bend the pin(s) slowly and deliberately, taking time to let the pin bend and not break due to trying to bend it too fast, just carefully "Work it" and you'll do OK.
I've actually fixed pins bent flat over and they work OK, that was the case with my FX 8320 when I got it brandnew out of the box!
Got the pin's tip where it needed to be and it went in no prob but it's been a "little" stubborn to install since.