With regard to the 2017 Presidential Inauguration attendance, NPR has published a good story on that topic and MSN offers some in-depth details about the video and photos being taken that day. Video of Trump’s claim that there were 1.5 million people attending is provided by a Washington Post report.
The following news release from Reuters provides a fairly accurate summary:
In an unusual and fiery statement on Saturday night, White House spokesman Sean Spicer lashed out about tweeted photographs that showed large, empty spaces on the National Mall during the ceremony on Friday.
“This was the largest audience ever to witness an inauguration, period. Both in person and around the globe,” Spicer said in a brief statement. “These attempts to lessen the enthusiasm about the inauguration are shameful and wrong.”
Washington’s city government estimated 1.8 million people attended President Barack Obama’s 2009 inauguration, making it the largest gathering ever on the Mall.
Aerial photographs showed that the crowds for Trump’s inauguration were smaller than in 2009.
Spicer’s rebuke followed a larger-than-expected turnout for women’s marches protesting Trump across the United States on Saturday, including at the flagship event in Washington, where a crowd of hundreds of thousands clogged the streets and appeared to be larger than those who came for Trump’s inauguration.
Spicer, who did not take questions from reporters, said spaces for 720,000 people were full when Trump took his oath.
As you can see from the photos below, it’s fair to say that Barack Obama’s inauguration drew a larger crowd, which suggests that claims from the Trump administration were false (the claim that theirs was the biggest inauguration ever). So for those making the point that the Trump administration exaggerated the number of people in attendance, the facts tend to support that point. We can see from the Reuters photos below, Barack Obama’s inauguration did not have any structures in the area where attendees were. So, there would have been no physical way possible for as many people to attend the Trump inauguration. The Trump administration eventually conceded to this fact.
For those really interested in comparing Tump’s inaugural turnout with Obama’s, there is an interactive crowd comparison tool provided by CNN that compares two images that were taken at about the same time during those respective events.