When using the Calypso editor to write a new post or page for a Jetpack connected site, only the last 20 images are available in the Media Library from the "Add Media" button. There is no way for a user to add previously uploaded images into their post or page.
Reported in 2441445-t.
I'm able to confirm this — it's not just images, but the last 20 "media items" including video, audio, and images.
Testing with a Jetpack site, themebreaker.wordpress.net — I see 50 items in wp-admin media library:

In Calypso I see only 20:

19May16 Bug Scrub
Confirmed this is still an issue. I can only see 20 out of 30 media items (all images in this case) from Calypso.
Confirmed again in 452463-chat #user-report
I confirmed this in a test today during a bug scrub. Added to Jetpack Sites / Posts Parity milestone, because if you move from WP.com to self-hosted — you'll immediately not have access to older uploaded files. That seems pretty bad.
Fixed in r145158-wpcom , Jetpack change sync pending at https://github.com/Automattic/jetpack/pull/5529
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Fixed in r145158-wpcom , Jetpack change sync pending at https://github.com/Automattic/jetpack/pull/5529