The weaknesses of Tennyson, in the text "In Memoriam," depend upon an individual reader's interpretation and understanding of the poem. Unfortunately, there will be some readers who believe, and support, that Tennyson showed no weakness in the poem. Others, those who disagree, will find numerous reasons regarding Tennyson's weaknesses in the poem. Therefore, it is hard to answer such a subjective question given an author's weaknesses are solely based upon an individual's response to the poem.
On a personal note, I do not see any weaknesses in "In Memoriam." The form of the poem follows a consistent rhyme scheme (abba cddc effe, and so on) and the poem is written in quatrains from beginning to end (four line stanzas). Technically, the poem follows a perfect form.
As for the message of the poem, one could easily support that Tennyson provides a distinct mood, one of sorrow and loss (as denoted by the title).
One problem that could be justified is the length of the poem. Tennyson could have, just as easily, written a poem that was much shorter and would not tend to overwhelm the reader. Unfortunately, the length of the poem mirrors Tennyson's own challenges in facing, and accepting, the death of his friend, Arthur Henry Hallam (which the poem depicts).