EDITS - I appreciate the comments and have incorporated them here. Thanks to @Superbest and @user22406 for raising them. I hope this makes a better answer for the community.
Under normal circumstances, genomic (self) or mtDNA released into your cell or body cause absolutely no (known) problems. I'll explain why that is, how the body can detect bacterial DNA, and finally the circumstances in which DNA can cause problems.
Self-DNA generally causes no problems
Almost from conception, cells in your body die. Sometimes as part of pre-programmed sequence (eg inter-digital cells of the fetal limb paddle die and form fingers) or normal replenishment of cells such as the white blood cell (hundreds of millions of neutrophils die each day) or your gut epithelium.
Macrophages consume liberated DNA, and the reticulo-endothelial system in the spleen, liver and lungs filters the blood for cellular fragments. This paper (from @Superbest) shows that bacterial DNA, and not normal human genomic DNA, can activate macrophages.
So your immune system develops, and is constantly being exposed to, virtually every cell type and cell component (proteins, lipids, DNA and RNA etc). If self-DNA could spark an immune reaction, normal life would be difficult. We don't make antibodies (from B-cells) or T-cells that react with self-components due to a process called anergy in which any developing T- or B- cells that could react to self-components during their maturation are instructed to shut down and/or die. Yes, mitochondrial are inherited matrilinearly, but they still lyse and cause anergy, preventing an auto-immune response.
(Not all cell death is harmless- @Superbest's comment reminds us that apoptosis (involved in finger formation and other tissue remodelling and cell turnover) can package cellular components into self-contained vesicles. On the other hand, damaged or lysed cells can liberate cytoplasmic components that can be pro-inflammatory or pro-coagulant.)
Macrophages' vacuoles contain DNAse II, an enzyme that degrades DNA it encounters following phagocytosing/endocytosing fragments of dead cells. More about that later....
Our bodies can detect bacterial DNA. Same DNA, different decoration
However, invaders (bacterial, viruses, worms etc) may activate a family of receptors called Toll-like receptors (TLRs). TLRs have evolved to have specificity for antigens not seen in mammals e.g cell walls, bacterial flagella and so on. Some TLRs do recognise DNA or RNA. You may know that DNA contains 4 nucleotide bases, A,T,G and C. In mammals, special sequences of two bases, C-G, (called "CpG"s) can be enzymatically modified by a methyl group. In bacterial CpGs are not typically methylated and so a TLR (e.g TLR-9) that detects un-methylated CpGs is generally detecting bacterial DNA.
Mitochondria are different
Mitochondria have features that resemble bacteria: a cell wall, a genome and the production of proteins that begin with the amino acid N-formyl-Methionine (f-Met). Mammalian proteins don't have f-Met at the start ("N-terminus"). Macrophages have a receptor that can recognize f-Met sequences (especially f-Met-Leu-Phe, fMLP) and activation of the fMLP receptor stimulates phagocytosis.
This 2013 paper describes the controversy whether mammalian mtDNA is methylated (at CpGs) and offers strong evidence that it is methylated. In contrast, the Oka paper gives 5 citations where mtDNA is not CpG-methylated.
So..do mitochondria look like bacteria to our innate immune system?
@user22406 flagged this paper by Oka et al which cites this paper by Zhang et al as evidence that mtDNA can be pro-inflammatory. The Zhang paper provides evidence that mitochondria can stimulate the immune system's receptors for (1) f-Met-peptides (i.e detecting mitochondrial proteins that look 'bacterial") and (2) receptors for un-methylated CpGs, the TLR-9 receptor. The Commentary on the article has a great figure of how mito components might promote inflammation which copyright prevents me adding.
The Oka paper uses 2 key techniques: (1) surgical constriction of the aorta to cause heart enlargement (cardiac hypertrophy) and (2) a mouse strain with the gene for DNAse II deleted (noted as -/-, two minuses, both alleles gone). In the hearts of DNAse II -/- mice, they observe higher levels of deposition of mtDNA in the damaged heart (Supplemental Fig 2), greater heart damage and many animals die. This suggests that excessive levels of DNA (not degraded in these DNAse -/- mice) may be driving the damage. (The general phenotype of DNAse -/- mice was studied by Kawane et al and the mice get an arthritis). In Oka's DNAse II -/- mice, the degree of heart damage can be reduced by blocking TLR-9 (using an inhibitory oligo). In aortic constricted mice where the DNAse II gene is intact (+/+), adding the TLR-9 blocking oligo gave some improvement, suggesting that the level of unmethylated DNA liberated in tissue damage may stimulate TLR-9 in normal animals.
The authors also examined aortic constriction in TLR-9 -/- mice and found they had less lung and heart damage compared to controls.
In summary, the Oka paper suggests something is signalling via TLR-9 to drive inflammation and damage in this model and implies (but does not prove) that the 'something' is mtDNA.
mtDNA in the plasma
Another Zhang paper detects up to 1ug/ml of mtDNA in the blood following major trauma (car and motorcycle crashes, falling 4 stories etc). Their paper shows that this level of liberated mitochondria could stimulate immune cells (via TLR-9 and f-Met receptor).
mtDNA won't get back inside the cell
Extracellular DNA and RNA is generally broken down and cleared rapidly. DNA, being a large, negatively charged molecule, will have extreme difficulty passing through an intact cell membrane. In the laboratory, cells need to be exposed to high voltage electric shocks to make transient 'pores' in the cell membrane to allow DNA to enter or have the DNA formulated in liposomes. Even if endocytosed, there is no known pathway to direct endocytosed DNA to the nucleus or an new mitochondrial 'host'. So mtDNA would be extremely unlikely to re-seed into a new cell or a mitochondria.
But self-DNA can be harmful if released in large quantities
During successful cancer chemotherapy, large numbers of tumor cells lyse and may give rise to tumor lysis syndrome. Among the products released when a tumor is killed is DNA. A and G - the 'purine bases' - can be further metabolized into uric acid. Uric acid can crystallize in the kidney and cause damage.
Mitochondria may be the remnants of endosymbiotic bacteria but, absent major trauma or mutations in both of your DNAse II genes, mitochondria come (and stay) in peace.