Hi David,
Have you placed the logo1.png file within the special www folder that sits inside the app folder?
Here's your code, which I'm executing on my computer.
library(shiny)
ui <- fluidPage(
titlePanel(title = span(img(src = "logo1.png", height = 35), "test"))
)
server <- function(input, output, session) {
}
shinyApp(ui, server)
The above code is saved as app.R within an app folder I have called shiny_example.

The www folder shown above contains a file called logo1.png

Thus, when I run the code, I get this:

Hope that helps. If not, please let me know.
All the best,
Hlynur