The birthday video Hodges watches is just over a minute long. When he plays it for the second time, he pauses only a few seconds in, but the video's progress bar is nearly at the halfway mark.
When Hodges watches the birthday video the second time, he pauses it with the mother and baby on the screen. He then hears a sound outside and the scene cuts to him looking out the window. Hodges then turns back to the computer and the paused video now just shows the birthday cake on a table.
During Brady's voiceover reading of the letter from Mr. Mercedes, and Hodges and Jerome's subsequent reading, they call the chat site "Under Debbie's Blue Umbrella". However, the letter itself (shown when Hodges first reads it) refers to the site as simply, "Debbie's Blue Umbrella".