I know that there are at least two Pslams omitted from the current Breviary, and I know that some pieces of others are missing (Psalm 136, for example, is missing the verse about dashing baby's skulls against rocks). I can't seem to find a reference to which Psalms and which verses are omitted.
The following is a list of omitted verses and Chapters from the four week plaster, currently in use. It follows modern numbering. Not Septuagint numbering.
Psalms Omitted Completely:
Verses Omitted from Particular Psalms:
Source: Psalms and Verses Omitted from the Four-Week Psalter Compiled by Fr. Felix Just, S.J., Ph.D.
Which Psalter specifically are you talking about? The Monastic Breviary? Roman Breviary (and which one specifically?) or the Novus Ordo Breviary (which uses the Nova Vulgata for its Psalter)?
As far as I am aware there is nothing missing; the whole point of praying the entire Psalter every week was to pray the full 150 psalms together.
Everything was included in the past; it was tradition to pray the entire 150 psalms. Now, granted some psalms were only prayed once, while some others might have been repeated. There were some weeks due to several festivities that they would not all be prayed, but this was largely restored after Leo XIII by re-fixing only very specific Saints who had a higher ranking. This was largely done in the Roman Breviary because this was never really a problem in the Monastic Breviary.
You can see the various versions of the Divine Office from pre-Tridentine all the way up to the "1960 Newcalendar" version here.