Looks to me like slugs or snails have been eating on your daylily folliage.

You have leaf miners. They have been very bad for the last couple of years. Use a systemic insecticide to control them.
Ed

Ed - Thank you for the information. Can you recommend a good systemic insecticide? Can you tell me when I should treat them? Is it okay to do so now while the plants are blooming? Should it be done in early spring? I would really appreciate any advice you can give me.

I used a generic 'Avid' this spring. I did a couple of applications about a week apart. You could also use 'Merit'. Treating the plants in the spring is much more effective than starting later in the season.

You could also use Bayer's 'All In One' or '3 in 1'. These products contain systemic insecticide, fungicide and fertilizer. You can also find them at most of the box stores. 'Avid' and 'Merit' are more commercially available.

You should be able to apply all with out harming bloom. With all sprays, it's better to spray after the plants have been watered and in the cooler part of the day.
Ed

Ed - Do you recommend that I wait until spring to apply? I'm trying to remove the foliage that looks to be infested.
I don't know that using the Bayer product now would be good since it has fertilizer included and many of my DL's have finished blooming for the year.

Thank you so much for this helpful information.