I think the comments raise two independent problems.
1. The mail() error – The noted URL points to "CiviCRM-Core-PR/684" with 2800+ tests completing (with 4 mail() related errors). Skimming through the other results in CiviCRM-Core-PR, this figure appears typical. I don't know why the mail() error arose, but – FWIW – it's not occurring anymore. (I've tried manually reproducing on the test-server and reviewing Jenkins-results from more recent days.)
2. The INFRA-124 deployment – This is basically replacing "tools/scripts/phpunit" with other tools (by baby-steps – ie transition "tools/scripts/phpunit" => "phpunit" => "paratest".) To reduce the pain, I've focused the effort on "CiviCRM-Core-Matrix" (for 4.5 & master). The most recent issue in the transition has been a parse-error (where phpunit produces slightly-malformed output) which causes CiviCRM-Core-Matrix#4.5 to display ~900 tests (rather than the expected ~3900 tests). The other versions/jobs (eg CiviCRM-Core-PR, CiviCRM-WebTest-Matrix) should be unaffected. Unfortunately, progress on this is rather slow (ie in the best case, one dev/feedback-cycle takes a couple hours; and we're not in the best-case because I'm juggling this with the other CiviCon/travel/sprint duties).
If we don't get it sorted this way in a couple days, then we can shift tactics – we can set CiviCRM-Core-Matrix back to using tools/scripts/phpunit, and we can setup separate jobs for INFRA-124 migration. It'd be a bit more laborious but would be appear smoother from your perspective.
In the past few days, we did a round of system updates ("apt-get upgrade") which could be the cause. Will investigate for a work-around...